Normally the formula for items in a circle is (n-1)! - in this case this is the 7!
It is multiplied by 2 because of the rest of the information. If you have the same arrangement of people you can have everyone shift one position to the right (or left) and they will be sitting next to a different person. With 2 shifts they will be back to sitting next to the original person.
Hope this helps.
If my response helps, please add throw me a kudos.
Jim Kernan is the Director of GMAT Operations at Stratus Prep and author of GMAT Materials for GMAT Prepster.