I need to see the statement to answer your question.
I think the sentence that uses it correctly is the last one.
The choice that best describes the word <em>enthusiasm </em>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:
apply the logical method to question above