Вычислите: \(-\frac{1}{12}\cdot\frac{3}{5}-\frac{2}{3}:\left(-\frac{10}{9}\right)\).

\[ -\frac{1}{12}\cdot\frac{3}{5}-\frac{2}{3}:\left(-\frac{10}{9}\right)= -\frac{1}{20}+\frac{2}{3}\cdot\frac{9}{10}= -\frac{1}{20}+\frac{3}{5}. \]

\[ -\frac{1}{20}+\frac{12}{20}=\frac{11}{20}. \]

Ответ: \(\frac{11}{20}\).