This question is totally based on power set concept.

Given, there are two finite sets having m and n elements.

Let Set1 has m elements and Set2 has n elements. 

Now, Power set of Set1 is

P(Set1) = 2^m 

and Power set of Set2 is

P(Set2) = 2ⁿ

According to question,

     2^m - 2ⁿ = 48

=> 2^m - 2ⁿ = 64 - 16

=> 2^m - 2ⁿ = 2⁶ - 2⁴

=> 2^m =  2⁶ and 2ⁿ = 2⁴

=> m = 6, n = 4