jmc

If we multiply the second equation, the reciprocal of the first equation, and the reciprocal of the third equation, we get $$\frac{s}{r}\cdot \frac{r}{q}\cdot \frac{t}{s}=6\cdot \frac{1}{9}\cdot 2\Rightarrow \frac{t}{q}=\boxed{\frac{4}{3}}.$$