C) a gerund phrase that functions as the subject of the sentence
The best description of the underlined phrase is the one that reads as follows: A gerund phrase that functions as the subject of the sentence. That is, your answer would be C.
A gerund is noun formed with a verb ending in -ing. Gerund phrases always start with a gerund, they include objects and modifiers, and they function as nouns (subject, object, subject complement). In this case, the gerund phrase "walking my dog" functions as the subject of the sentence.
