1. **Stating the problem:** Simplify the expression $$\frac{2m^2 - 2m - 24}{2m + 6} \div \frac{2m^2 - 32}{3m + 12}$$. 2. **Rewrite the division as multiplication by the reciprocal:** $$\frac{2m^2 - 2m - 24}{2m + 6} \times \frac{3m + 12}{2m^2 - 32}$$ 3. **Factor all polynomials where possible:** - Numerator of first fraction: $$2m^2 - 2m - 24 = 2(m^2 - m - 12) = 2(m - 4)(m + 3)$$ - Denominator of first fraction: $$2m + 6 = 2(m + 3)$$ - Numerator of second fraction: $$3m + 12 = 3(m + 4)$$ - Denominator of second fraction: $$2m^2 - 32 = 2(m^2 - 16) = 2(m - 4)(m + 4)$$ 4. **Substitute the factored forms back into the expression:** $$\frac{2(m - 4)(m + 3)}{2(m + 3)} \times \frac{3(m + 4)}{2(m - 4)(m + 4)}$$ 5. **Cancel common factors:** - Cancel $2$ in numerator and denominator. - Cancel $(m + 3)$ in numerator and denominator. - Cancel $(m - 4)$ in numerator and denominator. - Cancel $(m + 4)$ in numerator and denominator. 6. **After cancellation, the expression simplifies to:** $$\frac{1}{1} \times \frac{3}{2} = \frac{3}{2}$$ 7. **Final answer:** $$\boxed{\frac{3}{2}}$$ which corresponds to option C. This means the simplified form of the given expression is $$\frac{3}{2}$$.