What is the appropriate pronoun for this context: __________ met more than ten years ago at a mutual friend's graduation party.

The appropriate pronoun for the context provided is "She and I." This is because when referring to the subject of a sentence, the pronouns "she" and "I" are both in the nominative case, which is used for the subject performing the action.

In this sentence, "She and I" are the ones who met at the graduation party, functioning as the subject performing the action of the verb "met." Using "I" rather than "me" is crucial here, as "I" is the correct form when it is part of the subject of the sentence.

The other options either incorrectly use objective or possessive forms of the pronouns, which do not fit grammatically in the subject position of this sentence. Recognizing the proper use of pronouns in relationship to their grammatical roles is essential for constructing clear and accurate sentences.