Like most of Shakespeare's work, "Hamlet" presents several adolescent problems that could be considered universal. It is difficult to tell from your question if you seek the solutions that are presented in the play, or in general. It sounds like this is a brainstorming exercise that may lead to a compare/contrast essay.
Despite the fact that both Mel Gibson and Kenneth Branaugh were well into their 30s when they played fairly famous roles in Hamlet movies, keep in mind that in the original text of the play, we have to assume Hamlet is likely of adolescent age. Aside from his childish behavior (at times), it is known that he is still of school age, and is unmarried.
Keeping this in mind, I encourage you to brainstorm a list of the problems Hamlet experiences that are also common to other adolescent lives. Then, depending on the actual assignment, you can provide solutions that Hamlet tries, or solutions that are common to kids of that age.
To get you started, think about, then add to, the following:
- Problems with dating relationships and basic communication with members of the opposite sex (ie: Ophelia).
- Problems with school friends and honesty (ie: Rosencrantz and Guildenstern).
- Problems with open, honest relationships with parents.
- Experiencing death of a parent at a young age.
- Experience the remarriage of a parent at a young age.