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.