a) does not work as you need a 'to' ... and you haven't got one there! (You are allowed TO.....) b) works just fine. You are not allowed to leave.... c) works fine grammatically, but does not make sense. If you must stay to tidy up your books why would someone tell you to leave? So c) is not the answer. d) is fine. You are NOT being given PERMISSION to leave. You may not go. You must stay and tidy your books. So, b) and d) are grammatically correct AND make sense. c) is grammatically correct but does not make sense. a) is simply not right. Susan is actually right... you should tell us what YOU think! What YOUR choices would be, and why! But I hope this helps.

Tell us what you think and we'll correct you. Pay attention to the second sentence.

I think "may not" contains a meaning of "impossibility"( возможность ). But what the blank need is the meaning of "no permission". "may not" is different from "can not", i think.

I suppose that there're 2 answers: B), D). But I'm not quite sure of D)

The answer is B