75784 ÷ 6 = 12630 R4
Alright, let's work through the division of 75784 by 6 step by step.

Step 1:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 7 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 6

Step 2:
6 goes into 15 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 12 from 15 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 6

Step 3:
6 goes into 37 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 126
Subtract 36 from 37 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 6

Step 4:
6 goes into 18 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 1263
Subtract 18 from 18 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 6

Step 5:
6 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 12630
Subtract 0 from 4 to get 4.

The final result is 12630 with a remainder of 4.