The correct answer is B. Walking through the woods. Just like its name says, a participial phrase is a phrase (combination of a few words) where the headword is a present or past participle. Present participle can most easily be recognized by its ending (-ing), whereas past participle has -ed as the most common ending. You may wonder why the C option isn't a participial phrase. After all, it has a past participle (-ed). But you have to keep in mind that this is actually the simple past tense (made of past participle), which functions as a predicate. Therefore, the C option isn't a phrase, but a clause.
One detail in support of the argument against requiring community service is that it's time consuming.High schoolers are busy enough with their homework, studies and social life, let alone worry about doing community service in order to graduate.