Let's simplify the equation step by step:

2x + 3 - 6(x - 1) = 2(1 - x) - 7

First, distribute the -6 in the parenthesis on the left side of the equation:

2x + 3 - 6x + 6 = 2 - 2x - 7

Combine like terms on each side of the equation:

2x - 6x + 3 + 6 = 2 - 2x - 7
-4x + 9 = -2x - 5

Now, let's get all variables on one side and constants on the other side:

-4x + 9 + 2x = -2x - 5
-2x + 9 = -5

Subtract 9 from both sides:

-2x = -14

Finally, divide by -2 to solve for x:

x = 7

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