1. **State the problem:** Find the limit $$\lim_{x \to -2} \frac{x^2 - 4}{x + 2}$$. 2. **Recall the formula and rules:** When direct substitution leads to an indeterminate form like $$\frac{0}{0}$$, factor and simplify the expression. 3. **Evaluate the expression:** Substitute $$x = -2$$ directly: $$\frac{(-2)^2 - 4}{-2 + 2} = \frac{4 - 4}{0} = \frac{0}{0}$$ which is indeterminate. 4. **Factor numerator:** $$x^2 - 4 = (x - 2)(x + 2)$$ 5. **Simplify the limit expression:** $$\lim_{x \to -2} \frac{(x - 2)(x + 2)}{x + 2}$$ Cancel $$x + 2$$ (except at $$x = -2$$): $$\lim_{x \to -2} (x - 2)$$ 6. **Evaluate the simplified limit:** $$x - 2$$ at $$x = -2$$ is $$-2 - 2 = -4$$. **Final answer:** $$\boxed{-4}$$