The value of x is 4.
The external angle is equal to the sum of two opposite internal non-adjacent angles.
Using the exterior angle theorem,
m∠A = m∠B + m∠C
x + 2 = (3x - 6 ) + (2x -8)
x + 2 = 3x - 6 + 2x - 8
x + 2 = 5x - 14
2 + 14 = 5x - x
16 = 4x
Divide both sides by 4 we get
x = 4