The difference between the sum of 6 integers whose average is x and the sum of 3 numbers whose average is 2x-2 is?

The sum of the integers given the number of integers and their average is calculated by multiplying the number and the average. This is mathematically expressed as below,
                Sum = (n)(m)
where n is the number and m is the average or mean. 

For the first set,
              Sum = (6)(x) = 6x

For the second set,
               Sum = (3)(2x - 2)
                       = 6x - 6

If we are to subtract the second sum from the first,
       Difference  = (6x) - (6x - 6)
                          = 6x - 6x + 6

Hence, the answer is 6.