Explanation:

- The word "DETER" typically means to discourage or prevent someone from doing something.

- Option 1: "Excite" means to arouse or stir up feelings or reactions. It doesn't directly relate to discouraging or preventing, so it's not an antonym.

- Option 2: "Prevent" means to stop something from happening. It is not an antonym, but rather a synonym or similar in context to "deter."

- Option 3: "Dissuade" means to persuade someone not to take a particular course of action. It is similar to "deter," not an antonym.

- Option 4: "Encourage" means to give support, confidence, or hope to someone. It is indeed the opposite of "deter," making it the correct antonym.