If the length of an arc is 12π inches and the radius of the circle us 10 inches, what is the measure of the arc?

You're dealing with "arc length" here, and the formula for that is s = r*theta, where r is the radius and theta is the central angle in radians (not degrees).

Thus, s = (12pi inches) = (10 inches) (theta), so

theta = the central angle (not the measure of the arc) = (12pi) / (10 inches), or

theta = 1.2*pi (no units of measurement)