The correct answer is B. A noun
Step-by-step explanation:
A noun is a word that refers to a person, situation, object, etc. Due to this, in sentences, nouns commonly act as the subject or the object. Moreover, nouns can be composed if they include more than two nouns or other elements such as adjectives.
The phrase "the beloved family dog" is a noun because all of these words refer to a specific animal; moreover, this noun is compound as it includes two nouns "family", "dog" and one adjective "beloved". Besides this, you can know this is a noun because it acts as the subject of the sentence or the entity doing the action as the dog is the one that "loved to chase squirrels".