let's first convert the mixed fraction to improper, and then proceed.
[tex]\bf \stackrel{mixed}{2\frac{7}{10}}\implies \cfrac{2\cdot 10+7}{10}\implies \stackrel{improper}{\cfrac{27}{10}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{3}{5}\cdot \cfrac{7}{12}\div \cfrac{27}{10}\implies \cfrac{3}{5}\cdot \cfrac{7}{12}\cdot \stackrel{\stackrel{notice}{\downarrow }}{\cfrac{10}{27}}\implies \cfrac{3}{27}\cdot \cfrac{7}{12}\cdot \cfrac{10}{5}\implies \cfrac{1}{9}\cdot \cfrac{7}{12}\cdot \cfrac{2}{1} \\\\\\ \cfrac{1}{9}\cdot \cfrac{7}{1}\cdot \cfrac{2}{12}\implies \cfrac{1}{9}\cdot \cfrac{7}{1}\cdot \cfrac{1}{6}\implies \cfrac{7}{54}[/tex]