1. **State the problem:** Simplify the expression $10 - (4 + 2) \times 2$. 2. **Recall the order of operations:** Parentheses first, then multiplication, and finally subtraction. 3. **Calculate inside the parentheses:** $4 + 2 = 6$. 4. **Multiply:** $6 \times 2 = 12$. 5. **Subtract:** $10 - 12 = -2$. **Final answer:** $-2$