Question

Identify the choice that best describes the underlined word or phrase.

Answer 1

The choice that best describes the word enthusiasm is adverb phrase.
How was the suggestion greeted? With enthusiasm. 
Since adverbs are used to answer the questions how, when, where, etc., this too is an adverb phrase.
It cannot be an adjective - enthusiastic is an adjective.
Appositive phrase is set off by commas.
Gerund phrase is a verb that ends in -ing. 

Answer 2

Jim run for student body president was greeted with enthusiasm.Its an oppositive phrase.