Which is the largest number that will divide 1992 and 233 leaving remainders 12 and 13, respectively?

The number divides 1992 and 233 leaves the remainder 12 and 13 respectively. 

So, The number will divide (1992 - 12) and (233 - 13) completely. 

Now, The Largest number that will divide 1980 and 220 completely will be the HCF of these numbers. 

1980 = $$220\times\ 9$$

220 = $$220\times\ 1$$

So, 220 is the HCF and the number which will divides 1992 and 233 leaves the remainder 12 and 13 respectively. 

Hence, Option B is correct.