Составим выражение: \(5\frac{2}{9}:6\frac{4}{15}-1.2\).
\(5\frac{2}{9}=\frac{47}{9},\quad6\frac{4}{15}=\frac{94}{15},\quad1.2=\frac{6}{5}\).
\(\frac{47}{9}:\frac{94}{15}-\frac{6}{5}=\frac{47}{9}\cdot\frac{15}{94}-\frac{6}{5}=\frac{5}{6}-\frac{6}{5}=\frac{25-36}{30}=-\frac{11}{30}\).
Ответ: \(-\frac{11}{30}\).