You don't give us a lot of clues but I am guessing you are quite young (early teen?) and that you are not looking for some complicated situation. It is a useful piece of work to have been set because it is the sort of question that comes up when you have an interview for a job or, sometimes, for college places. They will want to know about real situations (though some people make them up anyway).
The sorts of things they want to know are:
Can you express yourself clearly?
Can you describe a challenging situation succinctly?
Can you analyse that situation to identify the underlying problem?
Can you reason out a possible solution? Is there more than one? Which is best?
Can you implement that solution? Do you show determination and resolve?
How do you deal with setbacks?
Can you think of a way you would check that the solution is working?
The challenge could be a simple disagreement with a friend, or the need to convince your parents about something you want to do or some physical or academic thing you want to achieve that you know won't be easy.
For example, I left school with very few qualifications. This prevented me getting interesting jobs or earning good money. My challenge was to break out of that situation by gaining more qualifications while still keeping a job. The solution was evening classes in subjects that were relevant to my field of interest and spending all my spare time studying. This led on to further study and to career advancement which provided the evidence that my solution worked.
Of course, there is whole lot more to it than that but that is just an outline. You'd need to think about all the incidental effects of your challenge and your solution ... and there can be many.
By the way, I wouldn't recommend what I did. It is much easier to learn when you are young, even though it doesn't feel like it at the time.
Good luck.