To solve this equation, we will first simplify both sides of the equation.

2(x-9):3 can be written as 2/3(x-9) = 2/3x - 6

3(x-6):4 can be written as 3/4(x-6) = 3/4x - 9/2

x+10:6 can be written as (x+10)/6

Now, we have the equation:

2/3x - 6 = 3/4x - 9/2 - (x+10)/6

To get rid of the fractions, we can multiply everything by 12 (the least common multiple of 3, 4, and 6):

12(2/3x - 6) = 12(3/4x - 9/2) - 12(x+10)/6
8x - 72 = 9x - 54 - 2(x+10)
8x - 72 = 9x - 54 - 2x - 20
8x - 72 = 7x - 74

Now, we can solve for x:

8x - 72 = 7x - 74
8x - 7x = 72 - 74
x = -2

Therefore, the solution to the equation is x = -2.