1. **State the problem:** We need to find a three-digit number with three different digits, where the ones place digit is 6, and the sum of the digits is 0. 2. **Analyze the problem:** The digits of a number are integers from 0 to 9. The sum of three digits being 0 means the sum of the digits equals zero. 3. **Important rule:** Since digits are non-negative integers (0 to 9), the sum of three digits cannot be zero unless all digits are zero. 4. **Check the conditions:** The ones place digit is 6, which is positive, so the sum of digits must be at least 6. 5. **Conclusion:** It is impossible for three digits (with one digit 6) to sum to zero. Therefore, no such number exists. **Final answer:** No such three-digit number exists with three different digits, a 6 in the ones place, and digits summing to zero.