52. \(\frac{2}{3}\) : \(\frac{6}{7}\) : \(\frac{4}{7}\)

1. First division: $$\frac{2}{3} : \frac{6}{7} = \frac{2}{3} \cdot \frac{7}{6} = \frac{14}{18} = \frac{7}{9}$$.
2. Second division: $$\frac{7}{9} : \frac{4}{7} = \frac{7}{9} \cdot \frac{7}{4} = \frac{49}{36}$$.
3. Convert to mixed number: $$\frac{49}{36} = 1 \frac{13}{36}$$.