1. **State the problem:** Calculate the value of the expression $10 \times (6 - (5 - 1))$. 2. **Understand the order of operations:** According to the rules of arithmetic, operations inside parentheses are performed first, starting from the innermost parentheses. 3. **Calculate the innermost parentheses:** $$5 - 1 = 4$$ 4. **Substitute back into the expression:** $$10 \times (6 - 4)$$ 5. **Calculate the next parentheses:** $$6 - 4 = 2$$ 6. **Substitute back and multiply:** $$10 \times 2$$ 7. **Final multiplication:** $$10 \times 2 = 20$$ **Answer:** The value of the expression is $20$.