Let's first simplify the left side of the equation:

1/2(1/3x - 1/4) = 1/6x - 1/8

Now, let's rewrite the given equation with this simplified expression:

1/6x - 1/8 = 2x - 3/2

Next, let's get rid of the fractions by multiplying both sides of the equation by 24 (the least common multiple of 6 and 8):

24(1/6x - 1/8) = 24(2x - 3/2)

4x - 3 = 48x - 36

Now, let's simplify further by combining like terms:

4x - 48x = -36 + 3
-44x = -33

Finally, divide by -44 to solve for x:

x = -33/-44
x = 33/44
x = 0.75

Therefore, the solution to the equation is x = 0.75.