1. **State the problem:** Simplify the expression $ (2x - 4) - (3x + 2) $. 2. **Write the expression:** $$ (2x - 4) - (3x + 2) $$ 3. **Distribute the minus sign to the second parentheses:** $$ 2x - 4 - 3x - 2 $$ 4. **Combine like terms:** $$ (2x - 3x) + (-4 - 2) $$ $$ = -x - 6 $$ 5. **Final answer:** The simplified expression is $-x - 6$. This matches the first option given.