The sum of the focal distances of the point$(4/\sqrt{5},3/\sqrt{5})$ on the ellipse $9x^2+4y^2=36$ is

Equation of the ellipse is $9x^2+4y^2=36\Rightarrow \frac{x^2}{4}+\frac{y^2}{9}=1(a<b)$.

Sum of the focal distances of the point $\left(\frac{4}{\sqrt{5}},\frac{3}{\sqrt{5}}\right)$ on the ellipse is its major axis $=2\left(3\right)=6$.