In normal case for circular arrangement in a table of 6 people we have (6-1)! = 120 arrangements.
Here, similar neighbor arrangement will be treated as same arrangement.
So, from 120 configuration, there will be pairs of configurations which will be considered same according to above condition.
So, total ans = 120/2 = 60.
example : say, three persons are sitting A - B - C in clockwise if we see from TOP of the table, and anticlockwise if we somehow visualize from the bottom of the table. In normal case : these two [ = (3-1)! = 2! = 2 ] arrangements are treated as different, But in this case we will consider only 1
