P is at distance $r=5\text{cm}=0.05\text{m}$ from each magnet's centre.

From the axial magnet (P on its axis): $B_1=\frac{{\mu }_0}{4\pi }\cdot \frac{2M}{r^3}$.

From the equatorial magnet (P on its equator): $B_2=\frac{{\mu }_0}{4\pi }\cdot \frac{M}{r^3}$.

The two field vectors are mutually perpendicular (one along the axial magnet's axis, the other antiparallel to the equatorial magnet's dipole). So:

$B_{net}=\sqrt{B_1^2+B_2^2}=\frac{{\mu }_0}{4\pi }\cdot \frac{M}{r^3}\sqrt{4+1}=\frac{{\mu }_0}{4\pi }\cdot \frac{M\sqrt{5}}{r^3}$.

Substituting $M=3\sqrt{5}$, $r^3=(0.05{)}^3=1.25\times 10^{-4}{\text{m}}^3$:

$B_{net}=10^{-7}\cdot \frac{3\sqrt{5}\cdot \sqrt{5}}{1.25\times 10^{-4}}=10^{-7}\cdot \frac{15}{1.25\times 10^{-4}}=10^{-7}\cdot 1.2\times 10^5=1.2\times 10^{-2}\text{T}$.

$B_{net}=12\times 10^{-3}\text{T}\Rightarrow \alpha =12$.