What I see in the first line, this phrase

    "how many unique arrangments (different people on left and right) how many arrangments are possible when seating 6?"


is not a formulation of a math problem.  It is rather somebody's fantasy.


The correct formulation is THIS:

    how many different arrangements are possible for 6 people seating in row ?


And then the answer is:  6! = 1*2*3*4*5*6 = 720.


Any of           6 in the most left position;
Any of remaining 5 in the next position;
Any of remaining 4 in the next position;
Any of remaining 3 in the next position;
Any of remaining 2 in the next position;
And for the last position there is only one possibility.


In all, there are 720 arrangements.