1. **State the problem:** Find the volume of a cylinder with height 6, width 12, and length 4. 2. **Identify the formula:** The volume $V$ of a cylinder is given by the formula: $$V = \pi r^2 h$$ where $r$ is the radius of the base and $h$ is the height. 3. **Clarify dimensions:** Usually, a cylinder is defined by its height and the radius of its circular base. Here, "width" and "length" likely refer to the diameter of the base. Since width is 12, the diameter $d = 12$, so the radius $r = \frac{d}{2} = \frac{12}{2} = 6$. 4. **Substitute values:** $$V = \pi \times 6^2 \times 6$$ 5. **Calculate:** $$V = \pi \times 36 \times 6 = 216\pi$$ 6. **Final answer:** The volume of the cylinder is $$216\pi$$ cubic units. This is the exact volume. If you want a decimal approximation, use $\pi \approx 3.1416$: $$216 \times 3.1416 \approx 678.58$$ cubic units.