1. **State the problem:** Evaluate the limit $$\lim_{x \to 4} \frac{x^2 - 16}{x - 4}$$. 2. **Recall the formula and rules:** When direct substitution in a limit results in an indeterminate form like $$\frac{0}{0}$$, we try to simplify the expression. 3. **Simplify the numerator:** Notice that $$x^2 - 16$$ is a difference of squares, which factors as $$ (x - 4)(x + 4) $$. 4. **Rewrite the expression:** $$ \frac{x^2 - 16}{x - 4} = \frac{(x - 4)(x + 4)}{x - 4} $$ 5. **Cancel common factors:** For $$x \neq 4$$, the $$x - 4$$ terms cancel out, leaving: $$ x + 4 $$ 6. **Evaluate the limit:** Now substitute $$x = 4$$: $$ 4 + 4 = 8 $$ **Final answer:** $$\lim_{x \to 4} \frac{x^2 - 16}{x - 4} = 8$$.