To solve this equation, we need to first simplify it by finding a common denominator for each fraction.

The common denominator for the fractions is 12, so we need to re-write the equation with all fractions having a denominator of 12:

(4x-4)/12 + (3x-9)/12 = (6x-2)/12 + (3x+3)/12

Next, combine like terms on each side of the equation:

(4x-4 + 3x-9) = (6x-2 + 3x+3)
7x - 13 = 9x + 1

Now, we can solve for x by isolating it on one side of the equation:

7x - 13 = 9x + 1
-13 = 2x + 1
-14 = 2x
x = -7

Therefore, the solution to the equation is x = -7.