In the interests of clarifying things, and saving my sanity, I thought I'd offer some background on how this problem came about and hopefully clarify where the ambiguities may have been introduced.
It all started when this Scientific American article (
https://www.scientificamerican.com/article/time-and-the-twin-paradox-2006-02/) came up in discussion - it claims to "explain" the twin paradox in terms of the time it takes for light to reach each observer. Now I claimed that this is misleading, because while the time delays might be interesting to consider in terms of what you'd actually "see", they are not relevant to the effects derived in Special Relativity. That is, time dilation and other effects are "real" and not just tricks due to how long it takes light to reach observers from distance events.
In order to demonstrate this, I pointed out that Einstein's original derivation let's observers have multiple clocks sitting in their frame of reference, all carefully synchronized with a clock next to them, and in this way the time it takes for light to reach each observer is eliminated (i.e., they measure the time of events in their frame by looking at their local clocks next to the event, no delay due to light propagation, or at least it's "cancelled").
This led to a number of progressively simpler thought experiments based on the twin paradox, trying to demonstrate this and other things that emerged in the process. Part of this involved having a fixed distance in A's frame (A was on Earth and the distance was to some star). Eventually we wound up with a situation like this:
A and B are two observers moving relative to each other at 0.6c
Two markers, 1 and 2, are stationary relative to A
As measured by A, the two markers are 6 light-years apart
When B's clock measures t = 0, B measures A as being next to marker 1 and himself as next to marker 2
When B's clock measures t = 0, B observers a pulse of light depart from A directed toward him
And the sticking point was how long it takes the light to reach B (3 years or 4.8 years?). I think that B would measure the distance between the markers as 4.8 light-years (the markers are stationary in A's rest frame, thus moving relative to B, so the 6 light-years apart markers are observed by B as length-contracted), but even if this is wrong, that doesn't matter for the next point: assuming he does measure the distance as 4.8 light-years, he will always measure the time it takes the light to reach him as 4.8 years by definition (or rather, by the two postulates of SR), regardless of the motion of A, or the motion of the markers, or anything else in the question -
if the light starts 4.8 light-years away as measured his frame, it takes 4.8 years to reach him.
Now hopefully you can see why the 6 light-years was called a "proper distance". The distance originally referred to actual things at rest relative to A. Unfortunately I made the colossal blunder of suggesting that we remove the markers from the description (oops) because I wanted to whittle thing down to core ideas, in particular the one above: that if B measures the light starting 4.8 light-years away then it will always take 4.8 light-years to reach him, regardless of how we got to that distance and the motion of B relative to A or the markers.
The other ambiguity of "setting A's clock to t = 0"... I wasn't really paying attention to :). I don't think it's relevant to the point above, which I what I really care about, so I'm happy to let A set his clock to t = 0 whenever he likes, and whatever that means, and whether A and B see whatever event was used to set t = 0 on their clocks as being simultaneous, doesn't matter - if we just care about knowing when B measures the pulse of light departing and we have the specified positions above. Nonetheless I can see how this lax phrasing would further confuse things.
But at the end of the day the thing I care about most is that the statement above hold regardless of anything else in the problem: "
if the light starts 4.8 light-years away as measured his frame, it takes 4.8 years to reach him"?