Is it permissible to back out of teaching two hours weekly that a teacher had agreed to teach on behalf of a colleague for the entire academic year, knowing that he was sincere at the time of the agreement? And is this backing out considered forbidden (haram), disliked (makrooh), or permissible (mubah)?

If what transpired between you and the manager falls under the category of a binding condition in the contract, then it must be fulfilled, and it is not permissible to retract it, for Allah Almighty says: "O you who have believed, fulfill [all] contracts," and the Prophet, peace and blessings be upon him, said: "Muslims are bound by their conditions." However, if it falls under the category of volunteering and assistance, then fulfilling it is recommended but not obligatory.