Formal:
* Acknowledge
* Admit
* Agree to
* Approve
* Concede
* Endorse
* Receive
* Take
Informal:
* Go for it
* Say yes
* Take it
* Buy into
* Be down with
Specific:
* Embrace (for welcoming something wholeheartedly)
* Tolerate (for accepting something reluctantly)
* Submit to (for accepting something with resignation)
* Yield to (for accepting something after resistance)
The best synonym to use will depend on the specific situation and the nuance you want to convey.