" 

 Actually, the word ""care"" in the above sentence is a noun.  ""Good"" and ""hairy"" are the adjectives the producers had in mind, but the questioner is right that ""his"" could be construed as an adjective.  It's actually both a possessive pronoun (possessive case of ""he"") and an adjective (modifying ""dog"").  The producers probably thought it was a pronoun and only a pronoun..."