The average of twelve numbers is 39. The average of the last five numbers is 35, and that of the first four numbers is 40. The fifth number is 6 less than the sixth number and 5 more than the seventh number. The average of the sixth and seventh numbers is:

44.5

Sum of 12 Numbers = 12 x 39

Sum of first four numbers = 4 x 40

Sum of last five numbers = 5 x 35

Sum of 5th, 6th and 7th numbers = 12 x 39 - 4 x 40 -35 x 5 =133

If 5th number is x then 6th number x + 6 and 7th number is x - 5

So 3x+1 = 132

x = 44

So, 6th number and 7th number are 50 and 39

and avg. = 44.5