We want to do the following multiplication:
[tex](-2\frac{5}{7})\cdot(-4\frac{2}{3})[/tex]Let's transform that into a normal fraction:
[tex]\begin{gathered} 2\frac{5}{7}=2+\frac{5}{7}=\frac{14+5}{7}=\frac{19}{7} \\ \\ 2\frac{5}{7}=\frac{19}{7} \end{gathered}[/tex]and the other fraction
[tex]\begin{gathered} \text{ 4}\frac{2}{3}=4+\frac{2}{3}=\frac{12+2}{3}=\frac{14}{3} \\ \\ 4\frac{2}{3}=\frac{14}{3} \end{gathered}[/tex]Therefore we can multiply the following fractions:
[tex]\begin{gathered} (-\frac{19}{7})\cdot(-\frac{14}{3}) \\ \\ \end{gathered}[/tex]The result is
[tex](-\frac{19}{7})(-\frac{14}{3})=\frac{19}{7}\cdot\frac{14}{3}=\frac{19}{1}\cdot\frac{2}{3}=\frac{38}{3}[/tex]Therefore
[tex](-2\frac{5}{7})\cdot(-4\frac{2}{3})=\frac{38}{3}[/tex]if we want we can write it in the same form as the others
Final answer
[tex]\frac{38}{3}=12\frac{2}{3}[/tex]