Perfect answers by chinnu and a_JOSHI....

Circular permutations of n objects are (n - 1) !..

Now, consider A,B,C,D,E,F,G to be the seven boys..

consider case of boy D..his neighbours are C and E..

In another arrangement, neighbours should be different..

Thus, both C-D-E  and E-D-C cant exist together..

So, for each boy,there are two arrangements wherein neighbours are the same..

So, (n-1)! has to be divided by 2..

Thus we get 6! / 2..