The sentence that uses a homophone correctly is: "Their going to the movies together."
Here's why:
1. "Their" is a possessive pronoun used to show ownership or belonging to a group of people. In this sentence, it correctly indicates that a group of people is going to the movies together.
2. Homophones are words that sound the same but have different meanings. In this case, "their" is a homophone for "there" and "they're."
By choosing the sentence that uses "their" correctly, you are identifying the homophone used appropriately in the given context.