Вычислим:
$$ \frac{9}{14} \cdot (\frac{17}{24} - \frac{5}{12}) = \frac{9}{14} \cdot (\frac{17}{24} - \frac{5 \cdot 2}{12 \cdot 2}) = \frac{9}{14} \cdot (\frac{17}{24} - \frac{10}{24}) = \frac{9}{14} \cdot \frac{7}{24} = \frac{9 \cdot 7}{14 \cdot 24} = \frac{9}{2 \cdot 24} = \frac{9}{48} = \frac{3}{16} $$Ответ: $$\frac{3}{16}$$