고 끝내다

do one last thing and finish

끝내다 is a person bringing something to an end, as against 끝나다, which is a thing ending by itself. The -고 clause is the final item before the close: 마지막 질문하고 끝내도록 하겠습니다 "I'll ask one last question and wrap up", 마지막 챌린지하고 끝낼까요? "shall we do the challenge and finish?". Most of these lines are a host signing off a video or a segment. In 나 이렇게 만들고 끝낼 거야!? it turns accusing — "you're leaving it like this and calling it done?".

Register: common as a sign-off