1. **State the problem:** Solve the equation $$4|2x + 3| + 8 = 20$$ for $x$. 2. **Isolate the absolute value:** Subtract 8 from both sides: $$4|2x + 3| + 8 - 8 = 20 - 8$$ $$4|2x + 3| = 12$$ 3. **Divide both sides by 4:** $$\cancel{4}|2x + 3| = \frac{12}{\cancel{4}}$$ $$|2x + 3| = 3$$ 4. **Recall the definition of absolute value:** If $|A| = B$, then $A = B$ or $A = -B$. 5. **Set up two equations:** $$2x + 3 = 3$$ $$2x + 3 = -3$$ 6. **Solve the first equation:** $$2x = 3 - 3$$ $$2x = 0$$ $$x = \frac{0}{2} = 0$$ 7. **Solve the second equation:** $$2x = -3 - 3$$ $$2x = -6$$ $$x = \frac{-6}{2} = -3$$ 8. **Final answer:** $$x = 0 \text{ or } x = -3$$