The correct answer is B. Up the mountain
Step-by-step explanation:
In grammar, a preposition refers to usually short words that link elements in a sentence and provide information about time, place, manner, etc. Examples of prepositions include after, about, over, up, before, on, into, etc. On the other hand, a prepositional phrase includes a preposition and any other word that modifies it that is usually a noun or pronoun. This implies in the sentence presented, the one that id a prepositional phrase is "up the mountain" because this includes the preposition "up" and the noun it modifies or "the mountain". So, the correct answer is B.