1. **State the problem:** Simplify the expression $(2x) + (-2x)$. 2. **Recall the rule:** Adding a number and its opposite (negative) results in zero. In algebra, $a + (-a) = 0$. 3. **Apply the rule:** $$ (2x) + (-2x) = 2x - 2x $$ 4. **Combine like terms:** $$ 2x - 2x = \cancel{2x} - \cancel{2x} = 0 $$ 5. **Final answer:** The expression simplifies to $0$.