Young Earth creationists can get away with lots of nonsensical claims about science when dealing with subjects that are complicated and hard to understand. For example they will argue that the different dating methods don't work, and are off by something like six orders of magnitude. Because this is a complex subject, many of their listeners believe it without much thought.
However, there's one aspect of physics that even creationists don't dare to question: The speed of light. (Which is curious, really, because the speed of light is exactly as esoteric and outside the realm of everyday life as is something like radioactive decay.)
Therefore young Earth creationists have a real problem with distant stars and galaxies, which are far, far beyond 6 thousand light-years away, being visible.
There are basically two schools of thought among them to explain it away: Some of them just make a vague statement that maybe God simply created everything at once and created the light on its way so that stars would be immediately visible. (They get a bit uneasy when asked why God would want to deliberately make the Universe look a lot older than it really is, according to them. Why the deception?) The other school of thought tries to twist physics and claim that physicists are either deluded or lying about the properties of light in the past. (No actual math is ever shown, of course. Just vague statements and waving of hands.)
The most common problem with both of them is that they seem to think that stars are just standing there, not doing much. However, that's not true. There's a lot of things happening in the observable Universe, and we can trace those events back a lot further in the past than just 6 thousand years.
SN 1987A is a wonderful example of this. It was a supernova event observed in 1987. This was a rather exceptional supernova in that it was surrounded at a great distance by a dust cloud (material ejected by another closeby stellar event in a very distant past.) Several months after the supernova the dust cloud was illuminated by its light.
Since we know the speed of light, we can therefore calculate the distance between the supernova and the dust cloud, and using simple triangulation we can calculate how far the supernova was from us. It turns out that it was approximately 168 thousand light-years from us.
In other words, that star exploded 168 thousand years ago, which is way before the alleged age of the Universe by the young Earth creationists. This is a problem for both schools of thought among them.
For the first ones, it brings into question God's honesty. If the Universe was indeed created just a bit over 6 thousand years ago, then God had to deliberately create light in such ways as to make it look like stellar events such as the SN 1987A have happened way, way before that. Why such a deception? Why is this alleged god lying to us?
For the second one, it becomes a physical impossibility. One common claim they make is that light was faster in the past. Even without going into the physics of that (there are many things wrong with that thought; for example, light slowing down affects redshift quite a lot) it just doesn't fit: For the most distant galaxies to be visible to us while still being just 6 thousand years old, light would have had to slow down by about six orders of magnitude (ie. about a million-fold.) That would mean that SN 1987A was actually about a million times farther from us, and therefore the explosion had to be about a million times brighter than it was. I think it's a physical impossibility for a supernova to be a million times brighter than supernovas observed today. Also the dust cloud would have to be a million times larger and have about a million times more matter in it. I think this would start making it about galaxy-sized (and would have quite a significant gravity.)
More importantly, though, if SN 1987A was a million times farther from us than what triangulation tells us, how far are the most distant galaxies then? They are way, way farther than SN 1987A. Which in fact creates vicious cycle: If all galaxies are really a million times farther than they look like, it means that light would have to had been even faster in the past (by another six orders of magnitude) in order for them to be visible... which means that SN 1987A was actually 12 orders of magnitude farther, and so on and so forth. You see the problem here? It just doesn't work.
It's actually quite amusing reading how young Earth creationists try to struggle with all these observations and explain them away.