Here's why:
* Prepositional phrases start with a preposition and end with a noun or pronoun (the object of the preposition).
* "With" is a preposition, but "long golden hair" acts as an adjective phrase describing someone or something. It modifies a noun, not a preposition.
Example:
* Sentence: The girl with long golden hair smiled.
* Prepositional phrase: "with long golden hair" (modifies "girl")
* Adjective phrase: "long golden hair" (modifies "girl")
Therefore, "with long golden hair" is an adjective phrase, not a prepositional phrase.