Most teenagers struggle to be free

Here, we're dealing with the correct idiom Both X and Y.

A. Both X but also Y is not idiomatic — we could have Both X and Y or Not only X but also Y, but this doesn't work. Eliminate.
B and C. Both X and also Y is redundant and not idiomatic. Eliminate.
D. Nothing wrong here.
E. We lose our idiom here, and it isn't clear what "their" refers to. Eliminate.

So D is our correct answer.

I'm curious where this question comes from: the use of "as well" in the correct answer is still somewhat redundant with "both", but it's the only answer option that works.