I maintain that the key to getting the sort by last names to work is first understanding why the sort by first names works.
(By *understanding* I mean, roughly, that you don't need to understand the gory details of the underlying sort algorithms Collections uses, but that
you should gain some appreciation of how
Java seems to "know" that you want the original list of Strings sorted in alphabetical order. Take a good look at the Collections class, especially the various sorting methods.)
If you search this forum, you should find several good threads on this assignment and sorting in general. But I'd recommend first taking another shot at figuring it all out on your own.