For a local rule question, you should start by drawing the new rule and making deductions:

G has to go after J, and R goes after G (rule 4). You need two spots, and there are only three open spaces for GR: 5, 6 and 7.
There are two possibilities:


Next, you need to place Q-S-Y. Q is before S, since Q isn’t third (rule 2).
QS can’t both go before J, because they can’t be beside each other. So Q goes before J, and S-Y go after.
Notice that there are four spaces after J, and now they’re filled by S-Y and G-R. Also note that S can’t go beside R.


S is forced to go in 4, so that it is not beside R and it is before Y.
Next, we have only Q and H left to place. H can’t go beside J, so H is in 1 and Q is in 2.


Now you just have to look at the answers and see which one is possible in one of these two diagrams.
E is CORRECT. All the other answers don’t work.

in your first placement of j-g-r you can deduce up front that H must be first when you place G 6th because H now can’t be next to both J and G which then forces the q-s-y grouping into their spots