1. **State the problem:** Evaluate the limit $$\lim_{x \to 6} \frac{x - 6}{x^2 - 4x - 12}$$ and simplify the answer. 2. **Factor the denominator:** $$x^2 - 4x - 12 = (x - 6)(x + 2)$$ 3. **Rewrite the expression:** $$\frac{x - 6}{(x - 6)(x + 2)}$$ 4. **Simplify the expression:** Since $$x \neq 6$$ in the limit process (except at the point of interest), we can cancel $$x - 6$$: $$\frac{1}{x + 2}$$ 5. **Evaluate the limit by substituting $$x = 6$$:** $$\frac{1}{6 + 2} = \frac{1}{8}$$ **Final answer:** $$\lim_{x \to 6} \frac{x - 6}{x^2 - 4x - 12} = \frac{1}{8}$$