General:
* Replied
* Responded
* Acknowledged
* Admitted
* Confirmed
* Explained
* Solved
* Resolved
* Fulfilled
* Met
Specific:
* For questions:
* Answered
* Explained
* Clarified
* Elucidated
* Illuminated
* For requests:
* Granted
* Fulfilled
* Acceded to
* For challenges:
* Met
* Overcame
* Conquered
* For accusations:
* Admitted
* Confessed
The best synonym to use will depend on the specific situation.