$a)3x\cdot \text{[?]}=6x^3{y}^2$

$6x^3{y}^2=2\cdot 3\cdot x\cdot x^2\cdot y^2=3x\cdot \underline{2x^2\cdot y^2}$

  $\left[?\right]=2x^2{y}^2$

$b)5p^{2}q\cdot \left[?\right]=\frac{1}{2}{p}^4{q}^{2}r$

$\frac{1}{2}{p}^4{q}^{2}r=\frac{5}{10}{p}^2\cdot p^{2}q\cdot q\cdot r=5\cdot \frac{1}{10}{p}^{2}q\cdot p^{2}qr=5p^{2}q\cdot \underline{\frac{1}{10}{p}^{2}qr}$

$\text{[?]}=\frac{1}{10}{p}^{2}qr$

 

$c)\frac{1}{3}a{b}^2\cdot \text{[?]}=-\frac{1}{9}{a}^4{b}^3$

$-\frac{1}{9}{a}^4{b}^3=\frac{1}{3}\cdot \left(-\frac{1}{3}\right)\cdot a\cdot a^3\cdot b^2\cdot b=\frac{1}{3}a{b}^2\cdot \underline{\left(-\frac{1}{3}{a}^{3}b\right)}$

$\text{[?]}=\left(-\frac{1}{3}{a}^{3}b\right)$

$d)\text{[?]}\cdot 0,125k{l}^{2}m=-16k{l}^3{m}^2$

$-16k{l}^3{m}^2=-\frac{128}{8}k{l}^2\cdot l\cdot m\cdot m=-128\cdot \frac{1}{8}k{l}^{2}m\cdot lm=-128\cdot 0,125k{l}^{2}m\cdot lm=0,125k{l}^{2}m\cdot \underline{\left(-128lm\right)}$

$\text{[?]}=\left(-128lm\right)$