Answer
The time difference between the two clocks is $7.92~ns$
Work Step by Step
Let $\Delta t_0$ be the time measured on the plane.
$\Delta t = \frac{\Delta t_0}{\sqrt{1-\frac{v^2}{c^2}}}$
$\Delta t_0 = \Delta t~\sqrt{1-\frac{v^2}{c^2}}$
$\Delta t_0 = (8.0~h)~\sqrt{1-\frac{(220~m/s)^2}{(3.0\times 10^8~m/s)^2}}$
$\Delta t_0 = 7.9999999999978~h$
We can find the time difference:
$8.0~h-7.9999999999978~h = 0.0000000000022~h$
$0.0000000000022~h = 7.92~ns$
The time difference between the two clocks is $7.92~ns$.
