4. \(3\frac{3}{4}\cdot\frac{2}{5}-3\frac{6}{25}\cdot\frac{5}{27}\)

Преобразуем смешанные числа: \(3\frac{3}{4}=\frac{15}{4}\), \(3\frac{6}{25}=\frac{81}{25}\).

\(\frac{15}{4}\cdot\frac{2}{5}=\frac{3}{2}\), \(\frac{81}{25}\cdot\frac{5}{27}=\frac{3}{5}\).

\(\frac{3}{2}-\frac{3}{5}=\frac{15-6}{10}=\frac{9}{10}\).

Ответ: \(\frac{9}{10}\).