For given current distribution, each infinite length wire produces magnetic field ‘B’ at origin then resultant magnetic field at origin ‘O’ is:

B_due to ∞ long wire = $\frac{{\mathrm{\mu }}_{\mathrm{o}}}{2\mathrm{\pi }}\frac{\mathrm{I}}{\mathrm{r}}$

At Origin, 

Magnetic field in along x axis is, ${\overrightarrow{B}}_x=2B\hat{i}$

and

Magnetic field in along y axis is, ${\overrightarrow{B}}_y=2B\hat{j}$

So, net magnetic field at origin is, $B_{net}=\sqrt{(2 B{)}^2+(2 B{)}^2}=2\sqrt{2} B$