A noun phrase is a phrase which has a noun or a pronoun as the nucleus and, gramatically, functions as a noun.
Considering this, we can conclude that the correct answer is C: "a relatively short time period" because the nucleus of that phrase is the noun "period".
The rest are not possible options because both A and B are independent clauses which do not complete the sentence but add new independent information, and D is not a noun phrase.
Soon his study ivory stride was heard as to and fro he paced and his old rounds upon planks so familiar to his tread that they were all over dented like geological stones with the peculiar mark
