Let’s take a look at the Korean sentence pattern Verb + 고 뭐 해(?). We normally say 뭐 해()? to ask someone what he does or what he is doing at the moment. In here, it doesn't mean anything like that. We use this to remind someone to start doing what he is supposed to do. If my friend is zoning out while having a meal, I would say Why are you not eating? (Stop zoning out and start eating). The main verb is 먹다 (to eat). Its negative form is 안 먹다. We take the verb stem and attach 고 뭐 해(). The actual sentence is 안 먹고 뭐 해?

We also use this to tell someone off for not doing what he is supposed to do. If I catch my son watching YouTube when he is supposed to be doing homework, I would say Why are you not doing your homework? (You are supposed to do your homework. Do it now). The main verb is 숙제하다 (to do homework). Its negative form is 숙제 안 하다. The actual sentence is 숙제 안 하고 뭐 해?

안 자고 뭐 해?

Why are you still up? (it’s already 4 in the morning)

나 안 깨우고 뭐 해?

Why didn’t you wake me up! I’m gonna be late because of you!

안 오고 뭐 해?

What are you waiting for? Let's go. (why are you not coming)