The correct answer is My favorite was a new board game called Sink the Ship.
Possessive pronouns replace a possessive adjective and a noun, for instance:
I will lend you my (possessive adjective) chair (noun).
I will lend you mine (pronoun in the possessive case).
Pronouns in the possessive case are: mine, yours, his, hers, its, ours, and theirs.
The sentences contain some instances of nouns in the possessive case such as Hansen's; or adjectives in the possessive case like my.