Insert a digit to make numbers that are divisible by 12 if it is possible 14…4

 Insert a 6.  The number divisible by 12 is  1464    

Step-by-step explanation:  Start by dividing 12 into the first two digits.

I am using old-fashioned long division.

       1  2

12 ) 14 6

     -12

         26.           this is the remainder, The next digit has to be a number that when divided by 12 will leave a remainder, that when paired with 4, will be evenly divisible by 12.

6 is that number . When you "bring down" the 6, you will be dividing 26÷12.  a  2 goes into the quotient, and in the next step 24 is subtracted from 26; the remainder is 2.

Bring down the 4 and divide 12 into 24.  The result is 2 as the quotient.  2 ×12 =24 .  24- 24 is 0

1464 ÷ 12 = 122