If M is performed on day 2, then it is also performed on day 7 (rule 2). We know that H can’t go first, because J has to go before H (rule 5). But there has to be one HM block, so therefore, H must go 6th.

Since M and O can’t be next to each other, O can’t go 1st, 3rd, 5th or 8th. Therefore it must go fourth. This proves that E is CORRECT.
As for the other variables, J can’t go 8th, since it has to be before H (rule 5), but otherwise, it can go first, third or fifth. As for G and L, they have no rules and can go anywhere.

A and B are wrong. The diagram shows that H must go 6th.
C is wrong. J could go on Day 1, but it doesn’t have to. You might have been tempted by this thinking that J has to be before H. The problem is that H goes quite late on this question, so any slot before 6th is fine for J. J doesn’t need to go before M.
D is wrong. L can go 8th, but doesn’t have to.

Why can’t O go 5th? There’s no M in 4/6
Why can’t 0 go in the fifth spot? H is in spot 6, so O wouldn’t necessarily be next to M. Am I missing a step?