Let's solve this equation step by step:

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

Expanding the parentheses:

3x + 4x - 6 = 8 - 7x + 14

Combining like terms:

7x - 6 = 22 - 7x

Adding 7x to both sides:

14x - 6 = 22

Adding 6 to both sides:

14x = 28

Dividing by 14 on both sides:

x = 2

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