Adjectival phrases modify nouns, which means that they usually stand next to a noun which they are describing. Having this in mind, the correct answer is B. A football game has four quarters of 15 minutes.
The prepositional phrase here is of 15 minutes, but it functions as an adjective phrase describing the noun quarters.
A is incorrect because the prepositional phrase acts as an adverbial phrase modifying the verb ends; C is incorrect because the prepositional phrase functions as an adverbial phrase modifying the verb supervised; D is incorrect because of the same reason - the phrase modifies the verb run.
