Ответ:

\(14-10\frac{7}{15}=\frac{210-157}{15}=\frac{53}{15}\).

\(\frac{1}{12}+\frac{2}{3}=\frac{1}{12}+\frac{8}{12}=\frac{3}{4}\).

\(\frac{53}{15}\cdot\frac{3}{4}=\frac{53}{20}=2\frac{13}{20}\).

Ответ: \(2\frac{13}{20}\).