Final answer:
The adverbial phrase among the choices is 'quite enthusiastically', as it modifies a verb to describe how an action is performed.
Step-by-step explanation:
In linguistics, an adverbial phrase ("AdvP") is a multi-word expression operating adverbially: its syntactic function is to modify other expressions, including verbs, adjectives, adverbs, adverbials, and sentences. Adverbial phrases can be divided into two types: complement adverbs and modifier adverbs.
An adverbial phrase is a group of words that acts as an adverb, modifying a verb, an adjective, or another adverb. It often indicates how, when, where, why, or to what extent an action is performed. Given the choices, 'quite enthusiastically' is an adverbial phrase. It modifies a verb by explaining how an action is being done, with the word 'quite' qualifying how enthusiastic the action is.
For example: Adverb: Pierre quickly ran through the main points of his argument ('quickly' modifies the verb 'ran'). Adverbial phrase: She threw down the gauntlet quite suddenly ('quite suddenly' is an adverbial phrase modifying the verb 'threw').