Final answer:
The prepositional phrase “with pink hair” is an adjective phrase modifying the noun “woman.”
Step-by-step explanation:
The prepositional phrase “with pink hair” in the sentence “He saw a young woman with pink hair” functions as an adjective phrase. This is because it is modifying the noun “woman”, describing which young woman he saw.
A prepositional phrase can function as either an adverb phrase or an adjective phrase, depending on what it is modifying. In the given sentence, "with pink hair" is a prepositional phrase and it is functioning as an adjective phrase. It is modifying the noun "woman", telling us more about her appearance.
If the phrase provided a time, place, or manner for the action of the verb (saw), then it would be considered an adverbial phrase. However, in this context, it's providing description for a noun and therefore is acting adjectivally.