멍석을 깔다 direct translations : to spread[lay out] a straw mat In this case, "멍석" is a kind of a platform to show something like a performance. It means "to make a place to do something" or "to make a arrangements". 멍석을 깔아줘도 못하냐? = 준비를 해줘도 못하냐? I rarely use it as a joke.

깔다 is a verb that has many,many meanings. Use with care