A participle is that form of the verb which partakes of the nature both of a Verb and of an Adjective.
A participle phrase will begin with a present or past participle. If the participle is present, it will dependably end in ing. Likewise a regular past participle will end in a consistent ed.
Since, all phrases require two or more words, a participle phrase will often include objects and/or modifiers that complete the thought.
Participle phrases always function as adjectives,adding description to the sentence.
In this case,
Option B is correct. The participle phrase 'clogged with dog hair' modifies the noun 'pipe'. The past participle 'clogged' introduces the participle phrase.
Options A and C are incorrect as they are devoid of any participle.
Option D is incorrect because the participle and the noun that it modifies have been punched together.