The participial phrase in this example is D - stored in the damp basement, as it is both a phrase (doesn't have a verb used with a certain person - stored is participle here, used as an adjective, not a verb) and it has this participle. In the previous options, A - we found - this is not a phrase, here verb is used as a verb, and thus it is a sentence, not a phrase. B - many of the old books - this is a noun phrase, it is about books. C - mold and mildew is an adjectival phrase. And thus, the only plausible answer here is D.
