A prepositional phrase that modifies a verb is used as an adverb. An adverb tells how, when, where, how much, and why. In sentence A, the prepositional phrase "around the racetrack" tells us where the red sports car sped.
The prepositional phrase in option B tells us which cat: the one "in the last cage". In option C the prepositional phrase describes the noun, house, when it says "with the green door". In option D the prepositional phrase "without nuts" tells us the type of chocolate she prefers.
