To solve this equation, we need to simplify the expression first:

2x - 3/6 - 4x + 5/12 = 0

Combine like terms:

(2x - 4x) - (3/6 + 5/12) = 0

-2x - (1/2 + 5/12) = 0

Now, to add the fractions, we need to find a common denominator, which is 12:

-2x - (6/12 + 5/12) = 0

-2x - 11/12 = 0

Next, we'll isolate the variable x by adding 11/12 to both sides:

-2x = 11/12

Now we divide by -2 to solve for x:

x = -11/24

Therefore, x = -11/24 is the solution to the equation.