1. The problem involves simplifying the expression $4\pi r^2 + 4\pi rh + 2\pi rh$. 2. We start by identifying like terms. The terms $4\pi rh$ and $2\pi rh$ are like terms because they both contain $\pi rh$. 3. Combine the like terms: $$4\pi rh + 2\pi rh = (4 + 2)\pi rh = 6\pi rh$$ 4. Now rewrite the expression with the combined terms: $$4\pi r^2 + 6\pi rh$$ 5. Factor out the common factor $2\pi r$ if desired: $$4\pi r^2 + 6\pi rh = 2\pi r(2r + 3h)$$ 6. This is the simplified form of the original expression. Final answer: $$4\pi r^2 + 4\pi rh + 2\pi rh = 2\pi r(2r + 3h)$$