1. **State the problem:** Solve the inequality $$(x+4)^2 - 4 < 0$$. 2. **Rewrite the inequality:** Add 4 to both sides to isolate the square term: $$ (x+4)^2 < 4 $$ 3. **Understand the inequality:** The square of a real number is less than 4 means the number itself lies between -2 and 2: $$ -2 < x+4 < 2 $$ 4. **Solve for $x$:** Subtract 4 from all parts: $$ -2 - 4 < x < 2 - 4 $$ $$ -6 < x < -2 $$ 5. **Interpretation:** The solution set is all real numbers $x$ strictly between $-6$ and $-2$. **Final answer:** $$ \boxed{-6 < x < -2} $$