A magnetic dipole having a magnetic moment of 0.72 A m^2 is placed...

When the north pole of a magnet points towards the geographic south, its magnetic moment $\vec{M}$ (directed from the south pole to the north pole of the magnet) points towards the geographic south.

The earth's horizontal magnetic field $B_H$ points towards the geographic north.

On the axial line, the magnetic field of the dipole $B_{axial}$ is in the direction of $\vec{M}$, which is towards the geographic south. Thus, $B_{axial}$ and $B_H$ are in opposite directions, and neutral points are obtained on the axial line.

At the neutral point, the magnetic field of the dipole equals the horizontal component of the earth's magnetic field:

$B_{axial} = B_H$

$\dfrac{\mu_0}{4\pi} \dfrac{2M}{d^3} = B_H$

Substituting the given values, $M = 0.72 \text{ A m}^2$ and $B_H = 18 \times 10^{-6} \text{ T}$:

$10^{-7} \times \dfrac{2 \times 0.72}{d^3} = 18 \times 10^{-6}$

$\dfrac{1.44 \times 10^{-7}}{d^3} = 18 \times 10^{-6}$

$d^3 = \dfrac{1.44 \times 10^{-7}}{18 \times 10^{-6}}$

$d^3 = \dfrac{1.44}{180} = 0.008 \text{ m}^3$

$d = \sqrt[3]{0.008} \text{ m} = 0.2 \text{ m} = 20 \text{ cm}$

The neutral points are located at a distance of $20 \text{ cm}$ on the axial line.