how many natural numbers have 20 as their digit's quotient and 11 as their digit's number??

If their digit's number means the sum of the digits, then there are lots of them.

But if since a quotient is only defined for two numbers, that implies that the number is a 2-digit value.

I can't think of any two digits whose quotient is 20 and whose sum is 11.

I suspect you have garbled the question.