$$24 - (3\frac{3}{5} - 1\frac{7}{9}) : (\frac{1}{2} - \frac{1}{3}) = 24 - (\frac{18}{5} - \frac{16}{9}) : (\frac{3}{6} - \frac{2}{6}) = 24 - (\frac{162}{45} - \frac{80}{45}) : \frac{1}{6} = 24 - \frac{82}{45} : \frac{1}{6} = 24 - \frac{82}{45} \cdot 6 = 24 - \frac{82}{15} \cdot 2 = 24 - \frac{164}{15} = \frac{360}{15} - \frac{164}{15} = \frac{196}{15} = 13\frac{1}{15}$$
Ответ: $$13\frac{1}{15}$$