Narrowed down to C & D, but both options have a redundant usage of "also" and "as well" respectively.
Let's examine the sentence and restructure it a bit:
Most adolescents stuggle to be free ... - ok that's given. Free of what? The underlined part starts off with "both" - which makes us expect
two entities which adolescents want their freedom from.
(C) - ... free both of X and also of Y
(D) - ... free both of X and of Y as well.
I must admit I can't argue on the validity of one statement over the other, but (D) presents both entities in succession and uses "as well" to establish the relationship laid down by "both".
Let us take another example:
1 - I want an admit both from XBS and also from YBS.
2 - I want an admit both from XBS and from YBS as well.
IMO, the "also" in (1) renders the usage of "both" redundant. Statement (1) could well have been stated as: "I want an admit from XBS and also from YBS" - no need to use "both".
Whereas, if we do use "both", the second statement sounds more appropriate.
I guess this was a classic ETS example of chosing from the lesser evil.