Instead of using --> if (letter.length() ==0)... and so on on line 25, could I use --> if (letter == "")...?

As a char can either be a letter or an int, in order to correctly handle a scenario where no input was received, Craig points out that "Strings have length". If the length is 0 which is a char, then no input was entered, not even a space. This serves two purposes: the first and most important is that if an entry is valid we can return letters.charAt(0), which gives us our char which is accepted by the original applyGuess method. Secondly, if the String has no length, the exception is thrown with the appropriate message.

Your first attempt will not work because you need to make sure that the new applyGuess(String) method will ultimately return a char so that it can be passed into the original applyGuess method, which accepts a char:

public boolean applyGuess(char letter)

Also, the way your attempt is written checks to see if letters is undefined rather than 0. Undefined does not mean the same thing as 0. The rest of our code at this point doesn't have any logic to handle an undefined letters variable and therefore when nothing is entered the application crashes instead of presenting the user with the desired exception message and the option to guess again.

I hope this makes sense...harder to put into words than I thought it would be :)

Liam has made a good point that undefined does not equal the same thing as 0. I would recommend sticking with the code below since it shows exactly what you mean.

if (letters.length() == 0)