Answer
$0.36\;\rm mm$
Work Step by Step
We know, in a double-slit experiment, that
$$\Delta y=\dfrac{\lambda L}{d}$$
where $\Delta y$ is the distance between two bright fringes, $L$ is the separation distance between the slit and the screen, and $d$ is the distance between the two slits.
Thus,
$$d=\dfrac{\lambda L}{\Delta y}$$
Plugging the known;
$$d=\dfrac{(600\times 10^{-9})(2)}{\frac{1}{3}\times 10^{-2}}=0.00036\;\rm m$$
$$d=\color{red}{\bf0.36}\;\rm mm$$
