In the sentence "Frank walked without any hesitation out the door. Identify the phrase in bold." the phrase in bold "without any hesitation" is an adverb phrase. Option D is correct.
An adverb phrase consists of a group of two or more words that function as an adverb in a sentence. The adverb is the head of the phrase. As well as a single adverb, a adverb phrase can modify a verb, adjective or another adverb. Adverb phrases generally answer the questions how, where, why or when something was done.