To solve this equation, we need to combine the like terms on the left side of the equation:

3x/4 + 5x/6 - 2x/3 = 13/12

To combine the fractions, we need to find a common denominator. The least common multiple of 4, 6, and 3 is 12.

Multiplying the first term by 3/3, the second term by 2/2, and the third term by 4/4, we get:

9x/12 + 10x/12 - 8x/12 = 13/12

Now, we can combine the fractions:

(9x + 10x - 8x) / 12 = 13/12

11x / 12 = 13/12

Now, we can solve for x by multiplying both sides by 12:

11x = 13

Dividing by 11:

x = 13/11

Therefore, the solution to the equation is x = 13/11.