Answer
$B = (-0.061~T)~\hat{k}$
Work Step by Step
The upward force on the particle due to the magnetic field must be equal in magnitude to the downward force due to gravity.
We can find the magnitude of $B$:
$qvB = mg$
$B = \frac{mg}{qv}$
$B = \frac{(0.010~kg)(9.8~m/s^2)}{(80\times 10^{-6}~C)(20\times 10^3~m/s)}$
$B = 0.061~T$
The velocity of the particle is in the +x direction and the force on the particle due to the magnetic field is in the +y direction. By the right hand rule, the direction of the magnetic field is into the page, which is the -z direction.
$B = (-0.061~T)~\hat{k}$
