6543 ÷ 6 = 1090 R3
Alright, let's work through the division of 6543 by 6 step by step.

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

Step 2:
6 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 5 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 6

Step 3:
6 goes into 54 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 109
Subtract 54 from 54 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 6

Step 4:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 1090
Subtract 0 from 3 to get 3.

The final result is 1090 with a remainder of 3.