Final answer:
The word 'She' in the sentence is a subjective case pronoun, functioning as the subject of the sentence.
Step-by-step explanation:
In the sentence "She has brown hair and green eyes." the pronoun 'She' is a subjective case pronoun. Subjective case pronouns include I, we, you, he/she/it, they, who, and whoever. These pronouns function as the subject of a sentence, meaning they are the person, place, thing, or idea that performs the action of the verb or about whom the sentence is. In this sentence, 'She' is the one who possesses brown hair and green eyes, thereby performing the action of having these characteristics.