The reason that the greatest possible sum of A, C and E is 6 instead of 9 is because of the limitation that A+C+E=B+D. Since the greatest value B and D can be is 3, the maximum value that the sum of B+D can be is 6.

If you set A,C, and E = 3; you'd basically say 3+3+3 = 9 = B+D, which isn't possible since the max of B+D is 6 and 9 > 6.