6564 ÷ 8 = 820 R4
Alright, let's work through the division of 6564 by 8 step by step.

Step 1:
8 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 8

Step 2:
8 goes into 65 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 64 from 65 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 8

Step 3:
8 goes into 16 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 82
Subtract 16 from 16 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 8

Step 4:
8 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 820
Subtract 0 from 4 to get 4.

The final result is 820 with a remainder of 4.