Let Z be the set of integers. $A=\left\{x\in Z;2^{\left(x+2\right)\left(x^2-5x+6\right)}=1\right\}$ and $B=\left\{x\in Z;-3<2x-1<9\right\}$ .If the number of subsets of the set $A\times B$ is 

$A=\left\{x\in z;2^{\left(x+2\right)\left(x^2-5x+6\right)}=1\right\}$

$\Rightarrow$$\left(x+2\right)\left(x-3\right)\left(x-2\right)=0$

$\therefore A=\left\{-2,2,3\right\}=3$elements

$B=\left\{x\in z;-3<2x-1<9\right\}\Rightarrow -1<x<5;x\in z$

$\therefore B=\left\{0,1,2,3,4\right\}=5$ elements

So  $A\times B$has $3\times 5=15$elements

$\therefore$No.of subsects in  $A\times B=2^{15}$