Final answer:
In the given sentence, 'your dog' fits the definition of a noun phrase, which is a noun and its modifiers.
Step-by-step explanation:
In the sentence 'Do you like playing fetch with your dog?', the noun phrase is 'your dog'. A noun phrase consists of a noun and all its modifiers, which can include adjectives or other nouns. In this particular sentence, 'your' is a possessive adjective modifying the noun 'dog', thus 'your dog' is identified as the noun phrase.
Learn more about Noun Phrase