The correct answer is b. skillfully.

In this sentence, "plays" is a verb and "volleyball" is the object of the verb. When an adverb is needed to describe how an action is performed, the adverb form of the adjective is used. In this case, "skillful" is the adjective form and "skillfully" is the adverb form. Therefore, the correct adverb form to describe how the action of playing volleyball is performed is "skillfully."