1. **State the problem:** Simplify the expression $2(m + 3)(m + 5) + 4(2m + 3)$. 2. **Use the distributive property:** Expand each product. $$2(m + 3)(m + 5) = 2[(m)(m + 5) + 3(m + 5)] = 2(m^2 + 5m + 3m + 15) = 2(m^2 + 8m + 15)$$ $$4(2m + 3) = 8m + 12$$ 3. **Multiply out the first term:** $$2(m^2 + 8m + 15) = 2m^2 + 16m + 30$$ 4. **Rewrite the entire expression:** $$2m^2 + 16m + 30 + 8m + 12$$ 5. **Combine like terms:** $$2m^2 + (16m + 8m) + (30 + 12) = 2m^2 + 24m + 42$$ 6. **Final answer:** $$\boxed{2m^2 + 24m + 42}$$