The partial circles at A and C mean those two angles are identical.
Because those two angles are identical sides AB and CB are the same length.
We can set those two equations to equal each other to solve for x:
x+4 = 3x-8
Add 8 to each side:
x+12 = 3x
Subtract 1x from each side:
12 = 2x
Divide both sides by 2:
x = 12/2
x = 6
Since AC is given as X, the length is 6
