Final answer:
The digits of 8.675 and 8.654 differ in the hundredths place, and 8.675 is the greater number because it has the higher digit in that place-value position.
Step-by-step explanation:
The greatest place-value position where the digits differ in the numbers 8.675 and 8.654 is the hundredths place. To determine this, we look at each place value and compare the digits. The tens, units, and tenths places are the same, but the hundredths place is different with 7 in the first number and 5 in the second number. Therefore, the number with the greater digit in the hundredths place, which is 8.675, is also the greater number overall.