Let's simplify the equation step by step:

7(3x-2) - (x-8) = 2(x+3)

First distribute the 7:
21x - 14 - (x-8) = 2*(x+3)

Distribute the negative sign:
21x - 14 - x + 8 = 2*(x+3)

Combine like terms:
20x - 6 = 2*(x+3)

Now distribute the 2:
20x - 6 = 2x + 6

Subtract 2x from both sides:
18x - 6 = 6

Add 6 to both sides:
18x = 12

Divide by 18 to solve for x:
x = 12/18
x = 2/3

So the solution to the equation is x = 2/3.