jmc

Dividing by $9$ lets us write the equation of the ellipse in standard form: $${\left(\frac{x}{3}\right)}^2+{\left(\frac{y}{3/2}\right)}^2=1.$$Thus, the length of the two axes of the ellipse are $2\cdot 3=6$ and $2\cdot \frac{3}{2}=3,$ so the distance between the foci is $\sqrt{6^2-3^2}=\boxed{3\sqrt{3}}.$