To solve the equation 2/3 + 3/4 x X = -5/6, we need to isolate the variable X.

First, let's simplify the equation by finding a common denominator for the fractions. The least common multiple of 3 and 4 is 12.

Multiplying the numerator and denominator of 2/3 by 4, we get 8/12.

Multiplying the numerator and denominator of 3/4 by 3, we get 9/12.

The equation becomes: 8/12 + 9/12 x X = -5/6.

Now, we can combine the fractions on the left side of the equation: (8/12) + (9/12) x X = -5/6.

To eliminate the fractions, we can multiply both sides of the equation by 12 to get rid of the denominators.

12 * (8/12) + 12 * (9/12) x X = 12 * (-5/6).

This simplifies to: 8 + 9x = -10.

Next, let's isolate the variable X by moving the constant term to the other side of the equation.

Subtracting 8 from both sides, we have: 9x = -10 - 8.

Simplifying further, we get: 9x = -18.

Finally, divide both sides of the equation by 9 to solve for X.

x = -18/9.

Simplifying the fraction, we have: x = -2.

Therefore, the solution to the equation 2/3 + 3/4 x X = -5/6 is X = -2.