Upon first reading of the sentence, the phrase "and it neighbored" should stick out as not idiomatic. Since the clause beginning with "a prehistoric" is background information about the Anasazi, we don't need the pronoun in the middle of it. We can eliminate (D) for the same reason.

The first apparent distinction between the remaining choices is "centered" and "that is centered." "Is" is incorrect since the culture is identified as prehistoric, so the present tense is wrong. That leaves us only with (B) and (C).

The difference is in the final few words of the underlined portion. The question is largely one of style. In (B), by placing the phrase "neighbored by the Hohokam" within "that is noted for distinctive pottery...," it places background information regarding geographic location in the middle of cultural details. In (C), "cultured centered...that neighbored the Hohokam, is..." places the comparison to the Hohokam's location alongside "the Southwest United States," which makes more logical sense. (C) is correct.