Well, I can see what approach you were trying to use. First of all, when you say "removing duplicates", are you only removing duplicates that are next to each other? In other words, you want to change "bookkeeper" to "bokeper" but "abcabcabc" doesn't get changed. If you want to return just "abc" for the second one, your whole approach is wrong.
Assuming you want to remove just the duplicates that are next to each other, you were sort of on the right track, but here's what you did wrong:
(1) When you go through looking at each character in userKeyword, like this:
for (lengthCounter=0; lengthCounter<wordLength; lengthCounter++){
if (userKeyword.charAt(lengthCounter) != userKeyword.charAt(lengthCounter + 1)){
you will get messed up if you change userKeyword inside the loop, as you did. The characters will shift over, but you'll keep incrementing the index, which means you will skip over some characters.
(2) Since you're looking at the characters at lengthCounter and lengthCounter+1, you have t be careful when you reach the end of the string. In this case, you don't want the index to reach the last character, because there is no character after it, and charAt(lengthCounter + 1) will crash. Change the for to say lengthCounter < wordLength-1.
(3) Finally, you're setting revisedKeyword and userKeyword to a one-character string.
String revisedKeyword = "" + userKeyword.charAt(lengthCounter);
userKeyword = revisedKeyword;
This certainly can't be what you want. You probably want to set up a new String to hold the entire keyword. Something like this: put this outside the loop
String newKeyword = "";
and then, to add a new character to it
newKeyword = newKeyword + userKeyword.charAt(lengthCounter);
and don't change userKeyword inside the loop; then at the end, newKeyword will be the answer.
(I'm assuming you need to learn how to use loops and stuff. In real life, I think I could do the whole thing in one line with a regex, but that's not the point of the exercise.)
String result = ""; for ... if not duplicate { result = result + charAt; } return result;