This game can be set like an ordinary group game with F, G, and H being our groups.
We are told that there are exactly 6 variables to be placed. And that H gets exactly 2 of them.
Already we are looking at something like this:
__ __ __ __ __ __ F G H
Taking into consideration some of the other rules, we can further realize that M is either in F or in G. It is prohibited from being in H. P and S are a pair always. At least one of L and Z are in F. The other can do as it pleases. And R is never mentioned, leaving it free.
This is the basic way to attack this game. You can make templates depending on what you feel would be most visually helpful to you. Either creating different templates showing the possibilities numerically, e.g. 1-3-2, 2-2-2, 3-1-2, or one template with M in F and another with M in G.
I hope this helps. Please let me know if you have any other questions.