Ответ:

\[\left(\frac{6}{11}+\frac{3}{22}\right)\cdot\frac{1}{15}=\left(\frac{12}{22}+\frac{3}{22}\right)\cdot\frac{1}{15}=\frac{15}{22}\cdot\frac{1}{15}=\frac{1}{22}.\]

Ответ: \(\frac{1}{22}\).