To form the greatest 8-digit number using the digits 5, 9, 3, 6, 7, and 4 by repeating the digits, we need to understand the rules of forming an 8-digit number and the place of the digit 6.

Rules for forming an 8-digit number:
1. The leftmost digit must be the greatest among all the available digits.
2. The remaining digits can be arranged in any order.

Finding the place of 6:
To determine the place of the digit 6, we need to compare it with the other available digits and find its position in the greatest possible arrangement.

Steps to find the place of 6:
1. Start by comparing 6 with the other digits in the thousands place (10,000).
2. The greatest digit available is 9, so 6 cannot be placed in the thousands place.
3. Move to the hundreds place (1,000) and compare 6 with the other digits.
4. The greatest digit available is 9, so 6 cannot be placed in the hundreds place.
5. Continue this process for the tens place (100) and the ones place (10).
6. In the tens place, the greatest digit available is 7, so 6 can be placed in the tens place.
7. Finally, in the ones place, the greatest digit available is 9, so 6 can be placed in the ones place as well.

Therefore, the place of 6 in the greatest 8-digit number is in the tens and ones place.

The greatest 8-digit number using the digits 5, 9, 3, 6, 7, and 4 by repeating the digits would be:
9,999,9976

In this number, 6 is repeated twice, once in the tens place and once in the ones place, and it is placed in the greatest possible position according to the rules of forming the number.

So, the place of 6 while forming the greatest 8-digit number is in the tens and ones place.