The correct answer is option (B):
a new hat
The correct answer is "a new hat." The sentence requires an article (a, an, the) before the noun "hat" because it is a countable noun. Since "hat" starts with a consonant sound, the indefinite article "a" is used. The adjective "new" describes the hat, and in English, adjectives generally come before the noun they modify. Thus, "a new hat" is grammatically correct and makes logical sense.