If F1 and F2 are the fourth proportional to

F1is the fourth proportional to $\frac{2}{7},\frac{7}{12},8$.
So,
F1=$ \dfrac{\frac{7}{12}\times 8}{\frac{2}{7}} $
= $ \dfrac{\frac{56}{12}}{\frac{2}{7}} $
= $ \dfrac{14}{3}\times\dfrac{7}{2} $
= $\dfrac{49}{3}$
F2 is the fourth proportional to $\frac{5}{6},\frac{4}{3},10$.
So,
F2=$\dfrac{\frac{4}{3}\times 10}{\frac{5}{6}} $
= $\dfrac{\frac{40}{3}}{\frac{5}{6}}$
= $\dfrac{40}{3}\times\dfrac{6}{5}$
= 16

Ratio:
F1:F2=$\dfrac{49}{3}:16 = 49:48$

49:48