5978 ÷ 6 = 996 R2
Alright, let's work through the division of 5978 by 6 step by step.

Step 1:
6 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 6

Step 2:
6 goes into 59 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 54 from 59 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 6

Step 3:
6 goes into 57 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 99
Subtract 54 from 57 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 6

Step 4:
6 goes into 38 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 996
Subtract 36 from 38 to get 2.

The final result is 996 with a remainder of 2.