The product of the roots of the equation $(\mathrm{x}-2{)}^2-3|\mathrm{x}-2|+2=0$ is

$\begin{array}{rl} & (\mathrm{x}-2{)}^2-3|\mathrm{x}-2|+2=0\\ \Rightarrow & |\mathrm{x}-2{|}^2-3|\mathrm{x}-2|+2=0\\ \Rightarrow & \left(\right|\mathrm{x}-2|-2)\left(\right|\mathrm{x}-2|-1)=0\\ \Rightarrow & |\mathrm{x}-2|=1,2\Rightarrow \mathrm{x}-2=\pm 1,\pm 2\Rightarrow \mathrm{x}=3,1,4,0\end{array}$

Hence, product of roots = 3 x 1x 4x0=0.