"Find favor" here is an idiom that means to be approved of or that he is pleased with her. "In your eyes" is a metaphor representing his evaluation. Alternate translation: "If you evaluate me and approve" or "If you are pleased with me" (See: [[rc://en/ta/man/translate/figs-idiom]] and [[rc://en/ta/man/translate/figs-metaphor]])
The abstract noun "petition" can be expressed with the verb "ask for." Alternate translation: "this is what I ask for" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])