 Solution

For a regular hexagon of side $a$, the perpendicular centre-to-side distance is $d=\sqrt{3}a/2$. Each side subtends endpoint angles with $\cos \beta =1/2$ and $\cos \alpha =-1/2$. Its centre field is consequently ${\mu }_{0}I/(4\pi d)$.

All six contributions have the same normal direction, soThe direction follows the current's right-hand rule. Equal side lengths alone would not fix an arbitrary distorted hexagon's field; the usual regular-coil geometry is used here.