Explanation

(c) The magnetic field outside the cylinder at point $P$ is
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B = \frac{\mu_{0}}{4\pi}\frac{2I}{r}$
And inside the cylinder at point $P$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B = \frac{\mu_{0}Ir}{2\pi R^{2}}$
At the axis $r = 0$
So, the magnetic field at the axis of the conductor is zero.