This is how I solved. Assume the radius of smaller circle r to be 2. then the area = PI (r)^2= Pi (2)^2 = 4 PI
Its also told that area of shaded region is 3 times the smaller circle = 12 PI
Now smaller circle + Shaded area = area of larger circle = 4Pi + 12Pi = 16 Pi
from this we can get the radius of Larger circle = Pi (R)^2 = 16 pi
cancelling pi from both sides = (R)^2 = 16 therefore R=4
Now that we know R we can find out Circumference of Larger circle = 2 PI R = 8 PI

Similarly we know the radius of smaller circle = 2 then Circumference of smaller circle = 4Pi
So to answer the main question that the circumference of the larger circle is how many times the circumference of the smaller circle?
= 8Pi / 4pi = 2 times = C

A quick confirmation - for circumference there is no subtraction of inner from outer circle required unlike that in area calculation? Thanks