As a native English speaker I'd take Duolingo's accepted answer (...only eats at the pagoda) to mean that the cook doesn't eat anywhere else but I know that someone is sure to point out that it literally means that when he is at the pagoda he does nothing but eat (only eats at vs. eats only at). This makes me wonder what the Vietnamese actually means.
My comment was about the literal meaning of the English, not the Vietnamese. Strictly speaking, "only eats at the temple" should mean "do nothing except eat when at the temple" while "eats only at the temple" clearly means "eats nowhere except at the temple. " English speakers often do not make this distinction but, if the latter is the actual meaning of the Vietnamese, Duo should at least accept the clearer, more logical English as correct.