1. Initial orbit

Let the initial distance of the satellite from the centre of the Earth be $r.$ Since the satellite is in a circular orbit, its orbital speed is $v=\sqrt{\frac{GM}{r}},$ where $M$ is the mass of the Earth.

So the initial angular momentum is $L = mvr = m\sqrt{\frac{GM}{r}}\,r = m\sqrt{GMr}.$

2. New distance from Earth centre

The statement says that the distance from the Earth centre is increased by eight times its initial value. Hence the new radius is $r' = 8r.$

3. Angular momentum in the new circular orbit

For a circular orbit at radius $r'$, the angular momentum is $L' = m\sqrt{GMr'}.$ Substitute $r' = 8r$: $L' = m\sqrt{GM(8r)} = \sqrt{8}\,m\sqrt{GMr} = \sqrt{8}\,L = 2\sqrt{2}\,L.$

4. Compare with options

The new angular momentum is $L' = 2\sqrt{2}\,L,$ which is not equal to $9L$, $8L$, $4L$, or $3L$.

So none of the given options is correct.

5. Check stored answer

Stored correct answer is D: $3L$.

But from gravitation for circular orbit, $L \propto \sqrt{r},$ therefore increasing orbital radius by a factor of $8$ gives $L' = \sqrt{8}\,L = 2\sqrt{2}\,L.$ Hence the stored answer is incorrect.