"scrambleWord" is a problem from the College Board's 2014 AP Computer Science A released exam. Let's take a look at it.
Get a copy of the problem from the College Board here. We're looking at problem #1 from that exam.
Take a look at solving problem (a), the scrambleWord method. Although the problem as a whole is relatively straightforward, this is the harder of the two methods that you'll be writing here.
When you've had a chance to look at part (a) and develop a preliminary solution, take a look at this explanation of one solution.
Next we'll take a look at part (b), the scrambleOrRemove method. Because this problem uses an ArrayList, you'll want to be sure you remember the methods that are useful for handling them. Check the College Board's Java Quick Reference which you should have a copy of for the test.
After you've tried to solve part (b), take a look at this solution.