First, convert into an improper fraction, then operate and simplify:
[tex]\begin{gathered} 3\frac{2}{8}\cdot\frac{9}{10}\rightarrow\frac{3\cdot8+2}{8}\cdot\frac{9}{10}\rightarrow\frac{26}{8}\cdot\frac{9}{10}\rightarrow\frac{13}{4}\cdot\frac{9}{10}\rightarrow\frac{117}{40} \\ \\ 2\frac{4}{10}\cdot\frac{4}{5}\rightarrow\frac{2\cdot10+4}{10}\cdot\frac{4}{5}\rightarrow\frac{24}{10}\cdot\frac{4}{5}\rightarrow\frac{12}{5}\cdot\frac{4}{5}\rightarrow\frac{48}{25} \\ \\ 1\frac{4}{12}\cdot\frac{2}{12}\rightarrow\frac{12+4}{12}\cdot\frac{2}{12}\rightarrow\frac{16}{12}\cdot\frac{2}{12}\rightarrow\frac{4}{3}\cdot\frac{1}{6}\rightarrow\frac{4}{18}\rightarrow\frac{2}{9} \\ \\ 3\frac{2}{3}\cdot\frac{2}{8}\rightarrow\frac{3\cdot3+2}{3}\cdot\frac{2}{8}\rightarrow\frac{11}{3}\cdot\frac{1}{4}\rightarrow\frac{11}{12} \end{gathered}[/tex]