Answer
${\bf 0.131}\;\rm T\tag{Out of the page}$
Work Step by Step
When the wire is levitated, the net force exerted on it is zero.
So,
$$\sum F_y=F_B-mg=ma_y=m(0)=0$$
where $F_e$ is the force due to the magnetic field.
Hence,
$$F_B=BIl=mg$$
Thus,
$$B=\dfrac{mg}{Il}$$
Plug the known;
$$B=\dfrac{(2\times 10^{-3})(9.8)}{(1.5)(0.10)}$$
And according to the right-hand rule, the direction of the magnetic field is out of the page.
$$ B=\color{red}{\bf 0.131}\;\rm T\tag{Out of the page}$$
