To solve for x in the equation 2x/3 + 3x - 1/6 = x/2, we first need to combine like terms and simplify the equation.

First, let's find a common denominator for the fractions in the equation. The common denominator for 3 and 2 is 6, so we can rewrite the equation as:

(2x*2)/(3*2) + 3x - 1/6 = x/2
4x/6 + 3x - 1/6 = x/2

Now, we can simplify the fractions:

(4x/6) + (3x) - (1/6) = (x/2)
(2x/3) + 3x - (1/6) = (x/2)

Next, we can combine the terms with x:

(2x/3) + 3x = (x/2) + (1/6)
(2x + 9x)/3 = (3x + 1)/6

Now, we can combine the terms on both sides of the equation:

11x/3 = 3x/2 + 1/6

To solve for x, we need to isolate x on one side of the equation. Let's first get rid of the fractions by multiplying both sides by 6:

6 * (11x/3) = 6 * (3x/2 + 1/6)
22x = 9x + 1

Now, subtract 9x from both sides:

22x - 9x = 9x - 9x + 1
13x = 1

Finally, divide by 13 to solve for x:

x = 1/13

Therefore, the solution to the equation 2x/3 + 3x - 1/6 = x/2 is x = 1/13.