14688 ÷ 4 = 3672 R0
Alright, let's work through the division of 14688 by 4 step by step.

Step 1:
4 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 4

Step 2:
4 goes into 14 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 12 from 14 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 4

Step 3:
4 goes into 26 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 36
Subtract 24 from 26 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 4

Step 4:
4 goes into 28 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 367
Subtract 28 from 28 to get 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 4

Step 5:
4 goes into 8 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 3672
Subtract 8 from 8 to get 0.

The final result is 3672 with a remainder of 0.