The noun "petition" refers to a formal request for another person to do something. It can be translated with a verb. The idiom "to give a petition" means to do what the person requests. Alternate translation: "has agreed to do what I solemnly requested that he do" (See: [[rc://en/ta/man/translate/figs-abstractnouns]] and [[rc://en/ta/man/translate/figs-idiom]])