46966 ÷ 4 = 11741 R2
Alright, let's work through the division of 46966 by 4 step by step.

Step 1:
4 goes into 4 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 4 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 4

Step 2:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 4 from 6 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 4

Step 3:
4 goes into 29 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 117
Subtract 28 from 29 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 4

Step 4:
4 goes into 16 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 1174
Subtract 16 from 16 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 4

Step 5:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 11741
Subtract 4 from 6 to get 2.

The final result is 11741 with a remainder of 2.