AHSME 1952 Problem 41

Increasing the radius of a cylinder by $6$ units increased the volume by $y$ cubic units. Increasing the height of the cylinder by $6$ units also increases the volume by $y$ cubic units. If the original height is $2$, then the original radius is: $\text{(A) } 2 \text{(B) } 4 \text{(C) } 6 \text{(D) } 6\pi \text{(E) } 8$