The correct option is C my
A word that can function as a noun phrase used by itself and that refers either to the participants in the discourse (e.g. I, you ) or to someone or something mentioned elsewhere in the discourse (e.g. she, it, this ) is a pronoun. In this case, the pronoun is indicating possession (towards the dog). Thus, we need a possessive pronoun in the blank. "My" and "Mine" are both possessive by nature. "My" is a possessive that is always used together with a noun, and is always used like an adjective (i.e. before the noun). "Mine" is a possessive that is never followed by a noun. The "dog" acts as the noun over here. Thus the answer is "my" Option C