The use of the pronoun "him," which should only be used as a sentence's object, is incorrect as a subject of the sentence. Thus, "him" needs to be changed to the third person subjective pronoun, "he;" therefore, "She and he were going to the dance after they had dinner," is the correct answer choice, as there are no other issues in the sentence.

The use of "I" in the object of the sentence is an absolutely incorrect usage, and needs to be fixed. The appropriate pronoun in the objective space is "me." As this is the only change that should be made to the sentence, the correct answer choice is "by both you and me."

The use of "she" in the sentence is incorrect, as "she" is a subjective pronoun and should only be used as the subject of the sentence. The pronoun should be changed to match "him," as an objective pronoun; therefore, the correct answer choice is "for both him and her."

The use of the pronouns "me" and "him" is incorrect, as both are in their objective forms, but are used as the subjects. Both pronouns need to be changed to their appropriate subjective forms. "He and I will always be" is the only answer choice that uses the correct pronoun forms.

The use of "I" as the object of the sentence is incorrect. There are no other issues in the sentence, so the only thing that needs to be done is to change "I" to the objective pronoun "me"; therefore, the correct answer choice is "The strongest supporter of the cause has been me."

The use of "me" in the subject of a sentence is always incorrect, as it is the first person objective pronoun. "Me" needs to be replaced by the first person subjective pronoun "I." Only one answer choice, "The major and I were always," makes this change, making it the correct answer choice.

Both pronouns in the underlined portion of the sentence, "he" and "I," are subjective pronouns, and should only be used as the subject of a sentence. Instead, they are used as objects of the sentence in question; each needs to be changed to its objective form. The answer choice that correctly uses both pronouns is "between me and him."

The use of "me," an objective pronoun, in the subject of a sentence is always wrong. In the subject, the first person pronoun should always be "I." Therefore, the correct answer choice is "The girls and I were."

The use of "me" in the subject of a sentence is always wrong, as it can only be used as the object of the sentence. The word "me" should be changed to the first person subjective pronoun, "I." The only answer choice that does this is "My friends and I have all taken."

The use of the objective pronouns "them" and "me" in the subject of a sentence is always wrong. Both pronouns need to be changed to their respective subjective pronouns "they" and "I." Thus, "They and I were going" is the correct answer choice.