The problem, as described by some of the comments in here is that the speed of light as percieved by different observers must always be the same (in a vacuum). So assuming you are the left planet, you will see the light coming at you at the speed 'c' over a distance of 8 meters which would take from your (and the sun's) perspective about 26.69 nano seconds. Now, in the second case, as you are moving away from the object, assuming the light beam is created as you exactly at 8 meters away, that light ray will have to come at you at the speed of light because of einsteins theory of relativity. So still that same 26.69 nanoseconds. And the same thing holds for the third case. However, because there are different velocities, there are different clocks and different notions of energy so the difference will be that the wavelength or colour of the light beam will be different.

On the flipside, someone at the sun will, in the second case, register a longer duration before the light ray hits you. It will in their perspective be longer than 26.69 ns but how much depends on the velocity at which you are moving.

In the third scenario, assuming both of you have the exact same velocity, it will be completely equivalent to the first scenario.