Ответ:

Преобразуем смешанные числа: \(3\frac{1}{6}=\frac{19}{6}\), \(5\frac{1}{6}=\frac{31}{6}\), \(4\frac{2}{15}=\frac{62}{15}\).

\(\frac{31}{6}:\frac{62}{15}=\frac{31}{6}\cdot\frac{15}{62}=\frac{5}{4}\).

\(\left(\frac{19}{6}-\frac{5}{4}\right)\cdot\frac{3}{92}=\left(\frac{38}{12}-\frac{15}{12}\right)\cdot\frac{3}{92}=\frac{23}{12}\cdot\frac{3}{92}=\frac{23}{368}\).

Ответ: \(\frac{23}{368}\).