\[\boxed{\mathbf{2.}\mathbf{314}}\]
\[\textbf{а)}\frac{7}{15} \cdot 5 = \frac{7 \cdot 5}{15} = \frac{7}{3} = 2\frac{1}{3}\]
\[\textbf{б)}\ 24 \cdot \frac{11}{48} = \frac{24 \cdot 11}{48} = \frac{11}{2} = 5\frac{1}{2}\]
\[\textbf{в)}\ \frac{5}{18} \cdot 12 = \frac{5 \cdot 12}{18} = \frac{5 \cdot 2}{3} =\]
\[= \frac{10}{3} = 3\frac{1}{3}\]
\[\textbf{г)}\ 6 \cdot 3\frac{5}{6} = 6 \cdot \frac{23}{6} = \frac{6 \cdot 23}{6} = 23\]
\[\textbf{д)}\ 2 \cdot 5\frac{2}{9} = 2 \cdot \frac{47}{9} = \frac{2 \cdot 47}{9} =\]
\[= \frac{94}{9} = 10\frac{4}{9}\]
\[\textbf{е)}\ 3\frac{5}{14} \cdot 7 = \frac{47 \cdot 7}{14} = \frac{47}{2} = 23\frac{1}{2}\]