1. **State the problem:** Evaluate the limit $$\lim_{x \to -7} \frac{\sqrt{x+8} - 6}{-3x - 12}$$. 2. **Identify the form:** Substitute $x = -7$ directly: $$\frac{\sqrt{-7+8} - 6}{-3(-7) - 12} = \frac{\sqrt{1} - 6}{21 - 12} = \frac{1 - 6}{9} = \frac{-5}{9}$$. 3. Since direct substitution gives a defined value, the limit is simply: $$\boxed{-\frac{5}{9}}$$. No indeterminate form appears, so no further simplification is needed.