Loudly knocking at the door, he demanded admission. The underlined part in this sentence is a/an -

An adverbial phrase is simply a group of two or more words that functions as an adverb in a sentence.
Just as an adverb can modify a verb, adjective or another adverb, an adverbial phrase can further describe a verb, adverb or adjective.
এখানে,
Loudly knocking at the door phrase টি ‘demanded’ verb টিকে modify করছে (expresses manner of demanding).
তাই এটি Adverbial phrase বলে গণ্য হবে।