The formula for volumes of cylinders, rectangular solids and prisms is the product of their height and base area or $h \cdot A$, where $h$ is there height and $A$ is their area, respectively.
Since a cylinder is a circle as its base, the area of its base is $\pi r^2$ and its volume is $\pi r^2 h$, where $h$ and $r$ are its height and radius, respectively.

Then we have A $= \pi (\frac{6}{2})^2 \cdot 12 = 108 \pi$ and B $= \pi (\frac{12}{2})^2 \cdot 6 = 216 \pi$.
Thus we have A < B.

Therefore, B is the right answer.