Select the word or phrase in the sentence that is not used correctly.

During the time he lived in New York, he worked as a writer, an editor, and a library.

In this sentence, the pronouns "He" and "I" are used correctly as the subjects of the sentence. When referring to multiple people, the subject pronouns "he" and "I" are used instead of the object pronouns "him" and "me." Therefore, option A is the correct choice.

Option B is incorrect because it uses "Him and I" instead of "He and I." Option C is incorrect because it uses "Me and him" instead of "He and I." Option D is incorrect because it uses "Him and me" instead of "He and I."

After throwing their sleeping bags into the backseat of their car, they drove more than 400 miles to reach their destination

The word "drove" is the past tense form of the verb "drive," which is appropriate for describing the action that occurred after they threw their sleeping bags into the backseat of their car. The sentence requires a past tense verb to maintain grammatical consistency. Therefore, option B is the correct choice.

The correct word or phrase to complete the sentence is "in spite of her dislike for the host."

She went to the party in spite of her dislike for the host.

Therefore, the correct answer is "D. in spite of."

The adverb "quickly" is the appropriate choice in this context to modify the verb "answering." It indicates the manner in which the action of answering should be done, emphasizing the need for speed or efficiency. The comparative forms "as quick" or "so quickest" are not necessary in this sentence.