The arc ST contributes 1/4 of the circle's total circumference, or 12pi/4 = 3pi.
We know that RS = RT = 6, so RA + AS + RC + CT = 6 + 6, but we also know that RA + RC = 8, so that AS + CT = 4.
B lies on the circle, which means RB = 6, which in turn means AC = 6.
So the total perimeter is 10 + 3pi, and the answer is (B).