1. **State the problem:** We need to multiply the values of the digit 9 in the number 9175.6 by the place value of the digit 6 in the number 26. 2. **Identify the value of 9 in 9175.6:** The digit 9 is in the thousands place. The place value of 9 is calculated as: $$9 \times 1000 = 9000$$ 3. **Identify the place value of 6 in 26:** The digit 6 is in the ones place. The place value of 6 is: $$6 \times 1 = 6$$ 4. **Multiply the two values:** $$9000 \times 6 = 54000$$ 5. **Final answer:** The product of the values is **54000**.