$a)\frac{1}{2}{x}^{2}yz\cdot 4y^{2}z=$   $\frac{1}{2}\cdot 4\cdot x^2\cdot y^{1+2}\cdot z^{1+1}=$   $2x^2{y}^3{z}^2$  

$2x^2{y}^3{z}^2\cdot \square =8x^3{y}^3{z}^3$  
$\square =8x^3{y}^3{z}^3:2x^2{y}^3{z}^2=$   $\left(8:2\right)x^{3-2}{y}^{3-3}{z}^{3-2}=4xz$  

$\frac{1}{2}{x}^{2}yz\cdot \square =8x^3{y}^3{z}^3$  

$\square =8x^3{y}^3{z}^3:\frac{1}{2}{x}^{2}yz=$