1. **State the problem:** Solve the inequality $12 - |2x| > 4$. 2. **Recall the properties:** The absolute value $|a|$ is always non-negative, and $|2x| = 2|x|$. 3. **Rewrite the inequality:** $$12 - |2x| > 4$$ which is $$12 - 2|x| > 4$$ 4. **Isolate the absolute value term:** $$12 - 2|x| > 4$$ Subtract 12 from both sides: $$\cancel{12} - 2|x| - \cancel{12} > 4 - 12$$ $$-2|x| > -8$$ 5. **Divide both sides by -2:** Remember, dividing by a negative number reverses the inequality sign. $$\frac{-2|x|}{\cancel{-2}} < \frac{-8}{\cancel{-2}}$$ $$|x| < 4$$ 6. **Interpret the absolute value inequality:** $$|x| < 4$$ means $$-4 < x < 4$$ **Final answer:** $$\boxed{-4 < x < 4}$$