Не принято решение, хотя по приведенным примерам всё пройдено

private boolean compressRow(int[] row) {
    boolean flag = false;
    for (int i = 0; i < row.length; i++) {
        if (row[i] == 0) {
            for (int j = 0; j < row.length; j++) {
                if (row[j] > 0) {
                    if (j != 0) {
                        int temp = row[j - 1];
                        row[j - 1] = row[j];
                        row[j] = temp;
                        flag = true;
                    }
                }
            }
        }
    }
    return flag;
}

import java.util.*;

public class Main {
    public static void main(String[] args) {
        int[] arr = new int[]{0, 4, 0, 0};
        System.out.println(Arrays.toString(compressRow(arr)));
    }
    private static int[] compressRow(int[] row) {
        for (int i = 0; i < row.length; i++) {
            if (row[i] == 0) {
                for (int j = row[i]; j < row.length; j++) {
                    if (row[j] > 0) {
                        if (j != 0) {
                            int temp = row[j - 1];
                            row[j - 1] = row[j];
                            row[j] = temp;
                        }
                    }
                }
            }
        }
        return row;
    }
}

private boolean compressRow(int[] row) {
        boolean flag = false;
        for (int i = 0; i < row.length; i++) {
            if (row[i] == 0) {
                //for (int j = 0; j < row.length; j++) {
                for (int j = i; j < row.length; j++) {
                    if (row[j] > 0) {
                        //if (j != 0) {
                            int temp = row[j - 1];
                            row[j - 1] = row[j];
                            row[j] = temp;
                        //}
                        flag = true;
                    }
                }
            }
        }
        return flag;
    }