1. **State the problem:** Simplify the expression $(-6)(-3) + (-6)(3)$ and verify the distributive property. 2. **Recall the distributive property:** For any numbers $a$, $b$, and $c$, $$a(b + c) = ab + ac$$ 3. **Calculate each product separately:** $$(-6)(-3) = 18$$ $$(-6)(3) = -18$$ 4. **Add the results:** $$18 + (-18) = 0$$ 5. **Use the distributive property on the right side:** $$(-6)[(-3) + 3] = (-6)(0) = 0$$ 6. **Conclusion:** Both sides equal 0, confirming the distributive property and the simplification. **Final answer:** $0$