Ratio question on parallel sides

Question

Besides of knowing the ratio of two sides is in proportion, I don't know how to go further.

Answer 1

Since the sides with arrows are pairwise parallel, we know $\frac{6a}{b}=\frac{8b}{3a}$.

Then cross multiply, we get $18a^2=8b^2$.

$\Rightarrow \frac{a^2}{b^2}=\frac{8}{18}=\frac{4}{9}$

$\Rightarrow \frac{a}{b}=\frac{2}{3}$ (since $a>0$ and $b>0$)

So, $a:b=2:3$