This question says O is performed on day 8, and L is performed on day 7. Anything on day 7 also goes second (rule 2), so L goes on day 2 as well:
HM is the most restricted variable, so we have to think where the HM block can go. Only the four slots in the middle are open. Further, H can’t go fifth since then it would also have to go 1st (rule 1). That wouldn’t leave space for J to go before H (rule 5).
So HM can only go 3rd and 4th, or 4th and 5th, and we now have 2 scenarios. In the first scenario we place HM in 3rd and 4th. In the second scenario, we place HM in 4th and 5th. In scenario 2, M also goes 1st because of rule 1.
Only G and J are left to place in each scenario. Note that both scenarios are now quite restricted: scenario 1 has three spaces and scenario 2 has two spaces.
In both scenarios, we must put J before H (rule 5). In scenario 1, this means J goes 1st, and also 5th (rule 1). In scenario 2, this means J goes third:
Both scenarios now only have a single space open: 6th. And both are missing a single variable, G. So, in both scenarios G must go sixth: A is CORRECT.
The incorrect answers are interesting. It may seem tempting to say J must go first. But, that is only true in scenario 1, so if you picked C, presumably you only found the first scenario. In that scenario, J does have to go first. The problem? In scenario 1, H also has to go third, and M has to go fourth. It isn’t possible for B, C and D to all be correct. So you can eliminate these answers for being contradictory.
(It’s possible you picked C because you thought J has to go before M, but that’s a mistake. J only has to go before H. It’s true that H is linked with M, but H can go before the second M. This leaves plenty of space for J to go before H. And if M goes twice, this allows the first M to be before J. You can see all of this illustrated in scenario 2, where the order is M – J – HM.)
So, scenario 2 eliminates B, C and D. As for E, scenario 1 proves that E doesn’t have to be true.
This is considered a very hard question, but it doesn’t need to be. The key is to go methodically through the steps and build two scenarios. Remembering that HM are the most restricted elements and using them to split the game into two scenarios is the key. Remember also to read the rules very carefully if you hit confusion on a question. Confusion often means there’s some error in the interpretation of the rules or you’ve missed one.