To solve this equation, let's simplify each side step by step.

Starting with the left side:

4 - ((6 - 2x) / 3) + x

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

= 4 - 2 + (2/3)x + x

= 2 + (5/3)x

Now, simplifying the right side:

2x - ((x + 3) / 2)

= 2x - (x/2) - 1.5

= 2x - (0.5)x - 1.5

= 1.5x - 1.5

Now, set the two sides equal to each other:

2 + (5/3)x = 1.5x - 1.5

To solve for x, first get rid of the fractions by multiplying by 3:

6 + 5x = 4.5x - 4.5

Now, isolate x by subtracting 4.5x from both sides and adding 4.5 to both sides:

6 + 5x - 4.5x = -4.5 + 4.5

0.5x = -2.7

x = -2.7 / 0.5

x = -5.4

Therefore, x = -5.4 is the solution to the equation.