This is how I solved it.
Total arrangements for 6 people (no restrictions) = 720
Leave M and J. For the rest 4 it is 4! = 24
Now M and J can sit together in the following ways
12, 23, 34, 45, 56 = 5 ways
Now since 12 is different from 21, we have 5x2 = 10 ways
So the 6 can be grouped with M and J sitting together is 24 x 10 = 240 ways
The 6 can be grouped without M and J sitting together is 720 - 240 = 480 ways
BTW, haddy, I do not think it is an easy question to answer. Compared to most of the standard ETS type perm/comb, I would rate this moderately difficult, if not too difficult. That said, I would not discourage you from reading more of perm/comb :-)