In which sentence does the prepositional phrase function as an adjective?
the man with the fancy yellow hat rode an old, beat-up bicycle
the man riding the old, beat-up bicycle wore a fancy yellow hat.
the man was wearing a fancy yellow hat when he left his house.
wearing a sheepish grin, the man rode his bicycle in the middle of the street.

The man with the fancy yellow hat rode an old, beat-up bicycle.

Explanation:

A prepositional phrase is a group of words that includes a preposition, its object (noun or a pronoun relating to another word), and words modifying the object. Prepositional phrases can function as nouns, adjectives, or adverbs. A prepositional phrase functioning as an adjective provides us with additional information about a noun or pronoun.

We can notice this in the example The man with the fancy yellow hat rode an old, beat-up bicycle. With the fancy yellow hat is a prepositional phrase that describes the noun man. We could've said The man rode an old, beat-up bicycle, but this phrase functioning as an adjective additionally describes the man, providing us with more details.