1. **Problem:** Solve the equation $|x + 2| = 4$. 2. **Formula and rules:** The absolute value equation $|A| = B$ means $A = B$ or $A = -B$ if $B \geq 0$. 3. **Apply the rule:** - $x + 2 = 4$ or - $x + 2 = -4$ 4. **Solve each equation:** - For $x + 2 = 4$, subtract 2 from both sides: $x = 4 - 2 = 2$ - For $x + 2 = -4$, subtract 2 from both sides: $x = -4 - 2 = -6$ 5. **Answer:** The solutions are $x = 2$ and $x = -6$. 6. **Check options:** None of the options exactly match $2$ and $-6$, but option (أ) is $6 - 4$ which equals $2$, and option (ب) is $1$ and $4$ which is incorrect. The correct solutions are $2$ and $-6$, so none of the given options are fully correct. **Final answer:** $x = 2$ or $x = -6$