$A=\{1,2\}$ and $B=\{3,4\}$

$\therefore A \times B=\{(1,3),(1,4),(2,3),(2,4)\}$

$\Rightarrow n(A \times B)=4$

We know that if $C$ is a set with $n(C)=m,$ then $n[P(C)]=2^{m}$

Therefore, the set $A \times B$ has $2^{4}=16$ subsets. These are

$\varnothing,\{(1,3)\},\{(1,4)\},\{(2,3)\},\{(2,4)\},\{(1,3)(1,4)\}$

$,\{(1,3),(2,3)\}$

$\{(1,3),(2,4)\},\{(1,4),(2,3)\},\{(1,4)(2,4)\},\{(2,3)(2,4)\}$

$\{(1,3),(1,4),(2,3)\},\{(1,3),(1,4),(2,4)\},\{(1,3),(2,3),(2,4)\}$

$\{(1,4),(2,3),(2,4)\},\{(1,3),(1,4),(2,3),(2,4)\}$