1. **State the problem:** Find the diameter of the base of a cone given its volume $V = 24\pi$ cubic feet and height $h = 2$ feet. 2. **Formula for the volume of a cone:** $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius of the base. 3. **Substitute known values:** $$24\pi = \frac{1}{3} \pi r^2 (2)$$ 4. **Simplify the equation:** $$24\pi = \frac{2}{3} \pi r^2$$ 5. **Divide both sides by $\pi$ to cancel it:** $$24 = \frac{2}{3} r^2$$ 6. **Multiply both sides by $\cancel{3}/\cancel{3}$ to clear the fraction:** $$24 \times \cancel{3} = \frac{2}{\cancel{3}} r^2 \times \cancel{3}$$ $$72 = 2 r^2$$ 7. **Divide both sides by 2:** $$\frac{72}{\cancel{2}} = \frac{2 r^2}{\cancel{2}}$$ $$36 = r^2$$ 8. **Take the square root of both sides:** $$r = \sqrt{36} = 6$$ 9. **Find the diameter:** $$\text{diameter} = 2r = 2 \times 6 = 12$$ **Final answer:** The diameter of the base is $12$ feet.