Final answer:
The digit that makes the number 866,4_6 divisible by 8 is 4, as the last three digits, 446, are divisible by 8 with no remainder.
Step-by-step explanation:
To determine a digit that makes the number 866,4_6 divisible by 8, one must remember that for a number to be divisible by 8, the last three digits of that number must also be divisible by 8. Looking at the number 866,4_6, we need to focus on the last three digits: 4?6. By trying different digits (0-9) in place of the question mark, we find that the digit 4 makes the last three digits, 446, divisible by 8.
The divisibility rule of 8 requires that the number formed by the last three digits when divided by 8 leaves no remainder. Therefore, 866,446 is divisible by 8 because 446 ÷ 8 equals 55 with no remainder, indicating successful divisibility by 8.