$9y \large\frac{dy}{dx}$$=-4x$
Integrating and using $y(0)=2$
We get equation of conic
$\large\frac{x^2}{9}+\frac{y^2}{4}$$=1$
here $a=3$
$b=2$
Length of latus rectum $=\large\frac{2b^2}{a}$
$\qquad=\large\frac{2 \times 4}{3}$
$\qquad=\large \frac{8}{3}$
Hence d is the correct answer.