6968 ÷ 6 = 1161 R2
Alright, let's work through the division of 6968 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 (9) of the dividend behind the 0 and repeat the process: 9 / 6

Step 2:
6 goes into 9 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 6 from 9 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 3:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 116
Subtract 36 from 36 to get 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 6

Step 4:
6 goes into 8 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1161
Subtract 6 from 8 to get 2.

The final result is 1161 with a remainder of 2.