Answer
The current in wire 2 is out of the page.
Work Step by Step
We can write the general expression for the magnetic field produced by a current in a straight wire:
$B = \frac{\mu_0~i}{2~\pi~R}$
If the net magnetic field at point $P$ is zero, the magnetic field at point $P$ due to each current must be equal in magnitude and opposite in direction.
By the right hand rule, the magnetic field at point $P$ due to the current in wire 1 is directed to the left. Then, the magnetic field at point $P$ due to the current in wire 2 must be directed to the right.
By the right hand rule, the current in wire 2 must be out of the page.
