1. **State the problem:** Simplify the expression $$\frac{16p^2 - 64q^2}{\frac{p^2}{\frac{4}{2} - \frac{8}{p}}}$$. 2. **Rewrite the expression:** The denominator is a complex fraction: $$\frac{p^2}{\frac{4}{2} - \frac{8}{p}} = \frac{p^2}{2 - \frac{8}{p}}$$ 3. **Simplify the denominator inside the denominator:** $$2 - \frac{8}{p} = \frac{2p - 8}{p}$$ 4. **Rewrite the entire denominator:** $$\frac{p^2}{\frac{2p - 8}{p}} = p^2 \times \frac{p}{2p - 8} = \frac{p^3}{2p - 8}$$ 5. **Rewrite the original expression:** $$\frac{16p^2 - 64q^2}{\frac{p^3}{2p - 8}} = (16p^2 - 64q^2) \times \frac{2p - 8}{p^3}$$ 6. **Factor the numerator:** $$16p^2 - 64q^2 = 16(p^2 - 4q^2) = 16(p - 2q)(p + 2q)$$ 7. **Factor the other factor:** $$2p - 8 = 2(p - 4)$$ 8. **Substitute back:** $$16(p - 2q)(p + 2q) \times \frac{2(p - 4)}{p^3} = \frac{32(p - 2q)(p + 2q)(p - 4)}{p^3}$$ **Final simplified expression:** $$\boxed{\frac{32(p - 2q)(p + 2q)(p - 4)}{p^3}}$$