To find the value of x, we can use the formula for the measure of an interior angle of a regular polygon. This formula states that for a regular polygon of n sides, the measure of each interior angle is equal to (n-2)*180/n degrees.
In this case, we can set n = 8, since the figure is an octagon. Therefore, the measure of each interior angle is equal to (8-2)*180/8 = 64°.
Substituting this into the equation (4x+12) = 64°, we get 4x = 52. Solving for x, we get x = 13. Therefore, the answer is OD. 13.