Let's simplify the left side first:

-4(x+2) + 3(x-1) - 2
= -4x - 8 + 3x - 3 - 2
= -x - 13

Now simplify the right side:

5(x-2) + 6
= 5x - 10 + 6
= 5x - 4

Now the equation becomes:

-x - 13 = 5x - 4

Add x to both sides:

-13 = 6x - 4

Add 4 to both sides:

-9 = 6x

Divide by 6:

x = -9/6
x = -3/2

Therefore, the solution to the equation is x = -3/2.