SOS, люди добрые) Код рабочий, валидатор ругается: Метод getBook в классе MarkTwainBook должен иметь тип возвращаемого значения MarkTwainBook и возвращать текущий объект.
public class Solution {
    public static void main(String[] args) {
        List<Book> books = new LinkedList<Book>();
        books.add(new MarkTwainBook("Tom Sawyer"));
        books.add(new AgathaChristieBook("Hercule Poirot"));
        System.out.println(books);
    }

    abstract static class Book {
        private String author;

        public Book(String author) {
            this.author = author;
        }

        public abstract Book getBook();

        public abstract String getTitle();

        private String getOutputByBookType() {
            String agathaChristieOutput = author + ": " + getBook().getTitle() + " is a detective";
            String markTwainOutput = getBook().getTitle() + " was written by " + author;

            String output = "output";

            if(this instanceof MarkTwainBook) output = markTwainOutput;//Add your code here
            if(this instanceof AgathaChristieBook) output = agathaChristieOutput;//Add your code here
            return output;
        }

        public String toString() {
            return getOutputByBookType();
        }
    }
    public static class MarkTwainBook extends Book {

        public String title;

        public MarkTwainBook(String author) {
            super("Mark Twain");
            this.title = author;
        }

        @Override
        public Book getBook() {
            return (MarkTwainBook) this;
        }

        @Override
        public String getTitle() {
            return title;
        }
    }
    public static class AgathaChristieBook extends Book {

        public String title;

        public AgathaChristieBook(String author) {
            super("Agatha Christie");
            this.title = author;
        }

        @Override
        public Book getBook() {
            return (AgathaChristieBook) this;
        }

        @Override
        public String getTitle() {
            return title;
        }
    }
}