Explanation:

- The original sentence is: "I would like to thank you for your coming out tonight."

- Option 1: "for comes out"

- This option is grammatically incorrect because it does not properly follow the structure after "thank you for."

- Option 2: "for you came out"

- This option is incorrect. "Came" is past tense, which disrupts the participle phrase needed here.

- Option 3: "for coming out"

- This is the correct choice. It uses the gerund "coming," which fits the structure appropriately and maintains the present continuous context for the event happening tonight.

- Option 4: "for you will come out"

- This option predicts future action, which is incorrect given that the context suggests addressing an action completed or occurring in the present.