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.
Answer: In The Way to Rainy Mountain, the most important insight Momaday gained about his heritage during his pilgrimage was how much the cultural identity of the Kiowas had declined over the span of his grandmother's life.
