Hey, there.
Sorry for the delay; your post slipped through the cracks.
This feels like an easy-ish game, but only if you're really good at picturing possible scenarios mentally (or willing to write them out).
Did you write out a complete scenario for C and one for E?
If not, that's ALWAYS what I do if I'm stuck wondering about answers. Once you write out a complete scenario, check it against the rules.
1: J F/J
2: no jazz
and then whenever we use rock, we can't have folk on the NEXT tape.
Let's see if we can come up with something for (C)
1: Jazz and Folk/Jazz
4: Folk and Rock
If I have folk on 4, I can NOT put rock on 3. How about I just put the other rock on tape 2?
1: Jazz and Folk/Jazz
2: Rock and ____
3: ____ and ____
4: Folk and Rock
What's left? Two hip-hop and the other half of Folk/Jazz from tape 1. How about
1: Jazz and Folk
2: Rock and Jazz
3: Hip-hop and hip-hop
4: Folk and Rock
Check the rules ... looks good. (Technically we could just pick C at this point, but let's analyze E).
1: Jazz and Folk/Jazz
2:
3: Folk and ____
4: Folk and ____
Okay, well that means that tape 1 is Jazz and Jazz, since I'm using both Folks elsewhere.
1: Jazz and Jazz
2:
3: Folk and ____
4: Folk and ____
The rule with Folk is that I can't have Rock on any tape that's 1 lower.
Since there's Folk on 4, I can't put Rock on 3.
Since there's Folk on 3, I can't put Rock on 2.
I can put one of my Rocks on tape 4, but where's the other one going to go?
This is why (E) breaks.
More formally, you might want to make sure you're thinking of that last rule as a conditional and writing out its contrapositive.
If rock is on a tape --> you can't have folk on the next tape
If you have folk on a tape --> you can't have rock on the previous tape
Hope this helps.