To solve this equation, we first simplify each side separately.

On the left side:
3x + 2/6 + 3x - 2/4
= 3x + 1/3 + 3x - 1/2
= 6x + 1/3 - 1/2
= 6x + 2/6 - 3/6
= 6x - 1/6

On the right side:
2x - 1/3 - 5/2
= 2x - 2/6 - 15/6
= 2x - 17/6

So our equation becomes:
6x - 1/6 = 2x - 17/6

Now, we want to solve for x. Let's subtract 2x from both sides:
6x - 2x - 1/6 = -17/6
4x - 1/6 = -17/6

Next, let's add 1/6 to both sides:
4x = -17/6 + 1/6
4x = -16/6
4x = -8/3

Finally, we divide by 4 to solve for x:
x = (-8/3) / 4
x = -8/12
x = -2/3

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