\[\boxed{\mathbf{2.}\mathbf{358}}\]
\[\textbf{а)}\ \frac{3}{4} \cdot \frac{4}{15} = \frac{3 \cdot 4}{4 \cdot 15} = \frac{1}{5}\]
\[\textbf{б)}\ 7 \cdot \frac{3}{7} = \frac{7 \cdot 3}{7} = 3\]
\[\textbf{в)}\ \frac{3}{8} \cdot \frac{1}{3} = \frac{3}{8 \cdot 3} = \frac{1}{8}\]
\[\textbf{г)}\ \frac{3}{5} \cdot 1\frac{2}{3} = \frac{3}{5} \cdot \frac{5}{3} = 1\]
\[\textbf{д)}\ 3\frac{3}{7} \cdot 2\frac{1}{3} = \frac{24}{7} \cdot \frac{7}{3} = \frac{24}{3} = 8\]
\[\textbf{е)}\ 2\frac{4}{7} \cdot 3\frac{1}{9} = \frac{18}{7} \cdot \frac{28}{9} = \frac{18 \cdot 28}{7 \cdot 9} =\]
\[= 2 \cdot 4 = 8\]