자고 하다

suggest doing something together

Reports a proposal — someone said 'let's.' 우리 팀에 부장님 스카우트 하자고 한 것도 황준현이고요 'Hwang Jun-hyun was the one who proposed scouting him', 나랑 밥 먹자고 하는 사람은 많아 'plenty of people ask me out to eat.' Because the original words were an invitation, it always means the speaker wanted the other person in on it, not simply that they gave an order. Drop the 고 and you get 자 하다, the same thing in faster speech.