1. **State the problem:** Solve for $n$ in the equation $$4^{2n+3} = 8^{n+5}.$$ 2. **Rewrite bases as powers of 2:** Since $4 = 2^2$ and $8 = 2^3$, rewrite the equation as $$\left(2^2\right)^{2n+3} = \left(2^3\right)^{n+5}.$$ 3. **Apply power of a power rule:** $$2^{2(2n+3)} = 2^{3(n+5)}.$$ 4. **Simplify exponents:** $$2^{4n+6} = 2^{3n+15}.$$ 5. **Since bases are equal, set exponents equal:** $$4n + 6 = 3n + 15.$$ 6. **Solve for $n$:** $$4n + 6 = 3n + 15$$ $$4n - 3n = 15 - 6$$ $$n = 9.$$ **Final answer:** $n = 9$ which corresponds to option D.