The correct option is C when
A conjunction's main function is to join or connect two clauses/sentences as one. In the given sentence, the clauses can be identified as "My hair was longer" and "I was younger", where the latter is the subordinate clause, as it depends on the main clause, the former, for its full meaning. The word that isn't a part of any of these clauses is 'when', hence it's determined that 'when' is a conjunction, it has no other role to play other than connecting the two and it's used for time-related sentences "was longer...I was younger" refers to the past. Hence, option C is correct. 'Hair' is a noun, it refers to the strands that grow on one's skin, particularly head, and does not join the clauses, it's a part of the main clause. Since it's a noun, option A is incorrect. "Longer" is an adjective that refers to the length of hair now, in comparison to the length of hair when she "was younger". It's not a conjunction, hence option B is incorrect. 'My' is a possessive adjective that modifies the noun 'hair', expressing possession of the girl's hair. It's not a conjunction, hence D is incorrect.