1. **State the problem:** Simplify the expression $\frac{3X+24}{-6}$. 2. **Formula and rules:** When dividing a sum by a number, you can divide each term separately by that number: $$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$$. 3. **Apply the rule:** $$\frac{3X+24}{-6} = \frac{3X}{-6} + \frac{24}{-6}$$. 4. **Simplify each term:** $$\frac{3X}{-6} = -\frac{3X}{6} = -\frac{X}{2}$$ and $$\frac{24}{-6} = -4$$. 5. **Combine the simplified terms:** $$-\frac{X}{2} - 4$$. **Final answer:** $$-\frac{X}{2} - 4$$.