We can assume $A = \{a\}$ and $B = \{a,b,c,d,e,f,g\}$ such that $n(A) * n(B) = 7$
Now $a \in K$.
$B \backslash A = \{b,c,d,e,f,g\}$ , here $2^6$ subsets are possible. Now $K$ must include elements from one of such $2^6$ subsets but it can not be $\phi$ nor $B \backslash A$.
There total no of possible $K$'s $= 64 - 2 = 62$
Total number of possible set is : 26 - 2 = 62