To solve the equation 3/4(x+1/2) - 5/6 = -1/4, we can follow these steps:

1. Distribute the 3/4 to the terms inside the parentheses:
(3/4)(x) + (3/4)(1/2) - 5/6 = -1/4

Simplifying the expression:
3/4x + 3/8 - 5/6 = -1/4

2. To combine the fractions, we need to find a common denominator. The least common denominator (LCD) for 4, 8, and 6 is 24. We can convert all the fractions to have a denominator of 24:

(3/4)x + (3/4)(1/2)(6/6) - (5/6)(4/4) = -1/4

Simplifying further:
(3/4)x + 18/24 - 20/24 = -1/4

3. Combine the fractions:
(3/4)x - 2/24 = -1/4

Simplify the fractions:
(3/4)x - 1/12 = -1/4

4. To eliminate the fractions, we can multiply the entire equation by the LCD, which is 12:

12[(3/4)x - 1/12] = 12(-1/4)

Simplifying:
9x - 1 = -3

5. Solve for x:
9x = -3 + 1
9x = -2

Divide both sides by 9:
x = -2/9

Therefore, the solution to the equation 3/4(x+1/2) - 5/6 = -1/4 is x = -2/9.