A magnetic dipole having a magnetic moment of 1.44 A m^2 is...

When the north pole of a magnetic dipole points towards the geographic north, its magnetic field on the equatorial line (the plane bisecting the dipole) is directed towards the geographic south. Since the horizontal component of the earth's magnetic field $B_H$ is directed towards the geographic north, the neutral points will lie on the equatorial line.

At the neutral point, the magnetic field of the dipole equals $B_H$:

$B_{eq} = B_H$

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

Substituting the given values:

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

$d^3 = \dfrac{1.44 \times 10^{-7}}{18 \times 10^{-6}} = \dfrac{1.44}{180} = 0.008 \text{ m}^3$

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

Thus, the neutral point is located at a distance of $20 \text{ cm}$ in the plane bisecting the dipole.