Answer
${\bf 2.0}\;\rm mT\tag{Into the page}$
Work Step by Step
The electron will be deflected upward toward the positive plate due to the electric field between the two plates. So we need a force that pulls him down by the same magnitude as the electric force.
This force is due to the magnetic field, which according to the right-hand rule must be directed into the page.
The two forces have the same magnitude.
$$F_E=F_B$$
$$qE=qvB\sin90^\circ$$
Thus,
$$B=\dfrac{E}{v}$$
where $E$ between two charged parallel plates is given by $E=\Delta V/d$
$$B=\dfrac{\Delta V}{vd}$$
Plug the given;
$$B=\dfrac{(200)}{(1\times 10^7)(1\times 10^{-2})}$$
$$B=\color{red}{\bf 2.0}\;\rm mT\tag{Into the page}$$
