Formal:
* Recognize: To identify and accept the existence of something.
* Admit: To confess or agree to the truth of something.
* Confirm: To state that something is true or correct.
* Verify: To check or prove the truth of something.
* Apprehend: To understand or grasp the meaning of something.
Informal:
* Notice: To become aware of something.
* See: To perceive something.
* Hear: To perceive something with your ears.
* Realize: To become aware of something suddenly.
* Appreciate: To show gratitude or recognition for something.
Specific to actions:
* Respond: To react to something.
* Answer: To reply to a question or request.
* Greet: To welcome someone.
* Salute: To show respect or honor.
* Acknowledge receipt: To confirm that something has been received.
The best synonym for "acknowledge" will depend on the specific context in which you are using the word.
For example, if you are talking about someone recognizing a person's presence, "notice" or "see" might be suitable. If you are talking about someone agreeing to the truth of something, "admit" or "confirm" might be better choices.