and I'm still not sure I fully understand it.

Back to my comp. theory classs, I'd say an example would be

X = B* (ie: Null, B, BB, BBB, BBBB, etc).
Y = B*C* (ie: Null, B, C, BC, BBC, BCC, BBCC, etc).

and the premise is for P which returns the set of all prefixes for a given language.

(Oops, we forgot a step, let's say our language is the element = {A, B, C})

The question you are asked to prove is
    Given P(X) is a subset of Y, is that equivalent to X is a subset of P(Y).

So, would P(X) == [A|B|C]*B*
and would P(Y) == [A|B|C]*B*C* ?