The correct option is D old, tattered hut
A noun phrase is a group of words containing a noun, and functions as a subject, object or object of preposition. In the given sentence, "old, tattered hut" is a phrase that contains two adjectives that modify the noun "hut"; hence it's a noun phrase and option D is correct. "I live" is a clause as it's made up of a subject and verb. Hence it's not a noun phrase and option A is incorrect. "Live" is a verb, it's not a noun phrase, hence option B is incorrect. "In an" is a prepositional phrase, not a noun phrase, hence option C is incorrect.