8 методов - по числу вариантов расположения слова относительно первой буквы слова (вверх (от первой буквы), вниз, влево, вправо и по варианты по диагоналям). Проверил разные варианты слов. Все верно пишет в список и выводит в консоль. Не могу понять почему не принимается валидатором. Либо лыжи не едут, либо мой глаз уже замылился. Код конечно получился длинный, зато читаемый на мой взгляд.
package com.javarush.task.task20.task2027;

import java.util.ArrayList;
import java.util.List;

/*
Кроссворд
*/
public class Solution {
    public static void main(String[] args) {
        int[][] crossword = new int[][]{
                {'f', 'd', 'e', 'r', 'l', 'k'},
                {'u', 's', 'a', 'm', 'e', 'o'},
                {'l', 'n', 'g', 'r', 'o', 'v'},
                {'m', 'l', 'p', 'r', 'r', 'h'},
                {'p', 'o', 'e', 'e', 'j', 'j'}
        };
        List<Word> listResult = detectAllWords(crossword, "home", "same", "masu", "meo", "nu", "npe");
        /*
Ожидаемый результат
home - (5, 3) - (2, 0)
same - (1, 1) - (4, 1)
         */
        for (Word x : listResult) {
            System.out.println(x);
        }
    }

    public static List<Word> detectAllWords(int[][] crossword, String... words) {
        List<Word> list = new ArrayList<>();
        for (String wordElement : words) {
            char[] wordToChar = wordElement.toCharArray();
            for (int y = 0; y < 5; y++) {
                for (int x = 0; x < 6; x++) {
                    findPattern(x, y, wordToChar, crossword, list);
                }
            }
        }
        return list;
    }

    public static Word findPattern(int x1, int y1, char[] wordToChar, int[][] crossword, List<Word> list) {
        Word objResult = null;
        if ((char) crossword[y1][x1] != wordToChar[0] || wordToChar.length == 1) return null;
        if ((char) crossword[y1][x1] == wordToChar[0]) {
            objResult = findPatternUp(x1, y1, wordToChar, crossword);
            if (objResult != null) list.add(objResult);
            objResult = findPatternDown(x1, y1, wordToChar, crossword);
            if (objResult != null) list.add(objResult);
            objResult = findPatternLeft(x1, y1, wordToChar, crossword);
            if (objResult != null) list.add(objResult);
            objResult = findPatternRight(x1, y1, wordToChar, crossword);
            if (objResult != null) list.add(objResult);
            objResult = findPatternLeftUp(x1, y1, wordToChar, crossword);
            if (objResult != null) list.add(objResult);
            objResult = findPatternLeftDown(x1, y1, wordToChar, crossword);
            if (objResult != null) list.add(objResult);
            objResult= findPatternRightUp(x1, y1, wordToChar, crossword);
            if (objResult != null) list.add(objResult);
            objResult = findPatternRightDown(x1, y1, wordToChar, crossword);
            if (objResult != null) list.add(objResult);
        }
        return null;
    }

    public static Word findPatternUp(int x2, int y2, char[] wordToChar, int[][] crossword ) {
        Word objResult = null;
        int lengthWord = wordToChar.length;
        int endX = x2;
        int endY = y2 - lengthWord + 1;
        int startX = x2;
        int startY = y2;
        if (endY < 0) return objResult;
        char endSymbolWord = wordToChar[lengthWord - 1];

        if (endSymbolWord == (char) crossword[endY][endX]) {
            for (int i = 1; i < lengthWord - 1; i++) {
                if (wordToChar[i] != (char) crossword[--y2][x2]) return objResult;
            }
            objResult = new Word(new String(wordToChar));
            objResult.setStartPoint(startX, startY);
            objResult.setEndPoint(endX, endY);
            return objResult;
        } else return objResult;
    }

    public static Word findPatternDown(int x3, int y3, char[] wordToChar, int[][] crossword ) {
        Word objResult = null;
        int lengthWord = wordToChar.length;
        int endX = x3;
        int endY = y3 + lengthWord - 1;
        int startX = x3;
        int startY = y3;
        if (endY > 4) return objResult;
        char endSymbolWord = wordToChar[lengthWord - 1];

        if (endSymbolWord == (char) crossword[endY][endX]) {
            for (int i = 1; i < lengthWord - 1; i++) {
                if (wordToChar[i] != (char) crossword[++y3][x3]) return objResult;
            }
            objResult = new Word(new String(wordToChar));
            objResult.setStartPoint(startX, startY);
            objResult.setEndPoint(endX, endY);
            return objResult;
        } else return objResult;
    }

    public static Word findPatternLeft(int x4, int y4, char[] wordToChar, int[][] crossword ) {
        Word objResult = null;
        int lengthWord = wordToChar.length;
        int endX = x4 - lengthWord + 1;
        int endY = y4;
        if (endX < 0) return objResult;
        int startX = x4;
        int startY = y4;
        char endSymbolWord = wordToChar[lengthWord - 1];

        if (endSymbolWord == (char) crossword[endY][endX]) {
            for (int i = 1; i < lengthWord - 1; i++) {
                if (wordToChar[i] != (char) crossword[y4][--x4]) return objResult;
            }
            objResult = new Word(new String(wordToChar));
            objResult.setStartPoint(startX, startY);
            objResult.setEndPoint(endX, endY);
            return objResult;
        } else return objResult;
    }

    public static Word findPatternRight(int x5, int y5, char[] wordToChar, int[][] crossword ) {
        Word objResult = null;
        int lengthWord = wordToChar.length;
        int endX = x5 + lengthWord - 1;
        int endY = y5;
        if (endX > 5) return objResult;
        int startX = x5;
        int startY = y5;
        char endSymbolWord = wordToChar[lengthWord - 1];

        if (endSymbolWord == (char) crossword[endY][endX]) {
            for (int i = 1; i < lengthWord - 1; i++) {
                if (wordToChar[i] != (char) crossword[y5][++x5]) return objResult;
            }
            objResult = new Word(new String(wordToChar));
            objResult.setStartPoint(startX, startY);
            objResult.setEndPoint(endX, endY);
            return objResult;
        } else return objResult;
    }

    public static Word findPatternLeftUp(int x6, int y6, char[] wordToChar, int[][] crossword ) {
        Word objResult = null;
        int lengthWord = wordToChar.length;
        int endX = x6 - lengthWord + 1;
        int endY = y6 - lengthWord + 1;
        if (endX < 0 || endY < 0) return objResult;
        int startX = x6;
        int startY = y6;
        char endSymbolWord = wordToChar[lengthWord - 1];

        if (endSymbolWord == (char) crossword[endY][endX]) {
            for (int i = 1; i < lengthWord - 1; i++) {
                y6--;
                x6--;
                if (wordToChar[i] != (char) crossword[y6][x6]) return objResult;
            }
            objResult = new Word(new String(wordToChar));
            objResult.setStartPoint(startX, startY);
            objResult.setEndPoint(endX, endY);
            return objResult;
        } else return objResult;
    }

    public static Word findPatternLeftDown(int x7, int y7, char[] wordToChar, int[][] crossword ) {
        Word objResult = null;
        int lengthWord = wordToChar.length;
        int endX = x7 - lengthWord + 1;
        int endY = y7 + lengthWord - 1;
        if (endX < 0 || endY > 4) return objResult;
        int startX = x7;
        int startY = y7;
        char endSymbolWord = wordToChar[lengthWord - 1];

        if (endSymbolWord == (char) crossword[endY][endX]) {
            for (int i = 1; i < lengthWord - 1; i++) {
                if (wordToChar[i] != (char) crossword[++y7][--x7]) return objResult;
            }
            objResult = new Word(new String(wordToChar));
            objResult.setStartPoint(startX, startY);
            objResult.setEndPoint(endX, endY);
            return objResult;
        } else return objResult;
    }

    public static Word findPatternRightUp(int x8, int y8, char[] wordToChar, int[][] crossword ) {
        Word objResult = null;
        int lengthWord = wordToChar.length;
        int endX = x8 + lengthWord - 1;
        int endY = y8 - lengthWord + 1;
        if (endX > 5 || endY < 0) return objResult;
        int startX = x8;
        int startY = y8;
        char endSymbolWord = wordToChar[lengthWord - 1];

        if (endSymbolWord == (char) crossword[endY][endX]) {
            for (int i = 1; i < lengthWord - 1; i++) {
                if (wordToChar[i] != (char) crossword[--y8][++x8]) return objResult;
            }
            objResult = new Word(new String(wordToChar));
            objResult.setStartPoint(startX, startY);
            objResult.setEndPoint(endX, endY);
            return objResult;
        } else return objResult;
    }

    public static Word findPatternRightDown(int x9, int y9, char[] wordToChar, int[][] crossword ) {
        Word objResult = null;
        int lengthWord = wordToChar.length;
        int endX = x9 + lengthWord - 1;
        int endY = y9 + lengthWord - 1;
        if (endX > 5 || endY > 4) return objResult;
        int startX = x9;
        int startY = y9;
        char endSymbolWord = wordToChar[lengthWord - 1];

        if (endSymbolWord == (char) crossword[endY][endX]) {
            for (int i = 1; i < lengthWord - 1; i++) {
                if (wordToChar[i] != (char) crossword[++y9][++x9]) return objResult;
            }
            objResult = new Word(new String(wordToChar));
            objResult.setStartPoint(startX, startY);
            objResult.setEndPoint(endX, endY);
            return objResult;
        } else return objResult;
    }

    public static class Word {
        private String text;
        private int startX;
        private int startY;
        private int endX;
        private int endY;

        public Word(String text) {
            this.text = text;
        }

        public void setStartPoint(int i, int j) {
            startX = i;
            startY = j;
        }

        public void setEndPoint(int i, int j) {
            endX = i;
            endY = j;
        }

        @Override
        public String toString() {
            return String.format("%s - (%d, %d) - (%d, %d)", text, startX, startY, endX, endY);
        }
    }
}