let's first of all, convert all the mixed fractions to improper fractions and then proceed.
[tex]\stackrel{mixed}{3\frac{4}{15}}\implies \cfrac{3\cdot 15+4}{15}\implies \stackrel{improper}{\cfrac{49}{15}} ~\hfill \stackrel{mixed}{6\frac{3}{10}}\implies \cfrac{6\cdot 10+3}{10}\implies \stackrel{improper}{\cfrac{63}{10}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{3\frac{4}{15}}{ ~~ 8\cdot 6\frac{3}{10} ~~ }\implies \cfrac{\frac{49}{15}}{ ~~ 8\cdot \frac{63}{10} ~~ }\implies \cfrac{\frac{49}{15}}{ ~~ \frac{252}{5} ~~ }\implies \cfrac{49}{15}\cdot \cfrac{5}{252}\implies \cfrac{49}{252}\cdot \cfrac{5}{15} \\\\\\ \cfrac{7}{36}\cdot \cfrac{1}{3}\implies \cfrac{7}{108}[/tex]