These grouping games with only two groups often lend themselves to creating multiple scenarios. If you do so properly, then you can move through this game very quickly. I am focusing on the first two rules at first.
M and P cannot be published in the same season. Because there are only two seasons, this gives us only two options.
F: M S: P or F: P S: M
Now let's consider our second rule. K and N must be published in the same season. Again, this yields two options that I will build into my diagrams.
1. F: M K N S: P
2. F: M S: P K N
3. F: P K N S: M
4. F: P S: M K N
I generally won't write more than 4 diagrams, so the combination of these two rules is perfect. I will now build in the other rules. Kf ---> Of Mf ---> Ns (If you'll notice, this rule eliminates my first diagram. Now we are down to 3.)
2. F: M S: P K N
3. F: P K N O S: M
4. F: P S: M K N
For each diagram, we have most of our placement solved. We just have to worry about L and O. If you can make a setup like this, you will breeze through the game.