A. Prepositional phrases modify nouns or verbs. Those which modify nouns are adjective phrases; those which modify verbs are adverbial phrases.
For example, The boy with the red hat wasn't very happy. "With the red hat" describes the boy. It tells which boy. Therefore it is an adjective phrase.
He hid the money under the bed. "Under the bed" tells where the money was hidden. It modifies the verb, so it is an adverbial phrase.