1. **State the problem:** Find the volume of a cylinder with radius $r=2$ cm and height $h=6$ cm. 2. **Formula for the volume of a cylinder:** $$V = \pi r^2 h$$ where $V$ is volume, $r$ is radius, and $h$ is height. 3. **Substitute the given values:** $$V = 3.14 \times 2^2 \times 6$$ 4. **Calculate the radius squared:** $$2^2 = 4$$ 5. **Multiply the values:** $$V = 3.14 \times 4 \times 6$$ 6. **Calculate intermediate multiplication:** $$3.14 \times 4 = 12.56$$ 7. **Final volume calculation:** $$V = 12.56 \times 6 = 75.36$$ 8. **Round to the nearest tenth:** $$V \approx 75.4$$ cm$^3$ **Answer:** The volume of the cylinder is approximately 75.4 cm$^3$, which corresponds to option C.