Well, I've seen three excuses.
(1) God created the light in transit. This means, of course, that when you see (for example) a supernova more than a few thousand lightyears away, you're watching something that hasn't actually happened, and the universe is literally one giant fake.
(2) The light ran most of the way, but then slowed down, because ... er ... look, a bunny! This would break a few laws of physics, but creationists don't really like the laws of physics anyway, look at their longstanding grudge against thermodynamics.
(3) The stars aren't really that far away. Of course, if you compressed all the galaxies we can see into a sphere only 6000 lightyears in radius we'd all be dead, but this is a mere detail.
It is of course possible to combine either of the first two with the third in a sort of belt-and-braces approach to reality denial.
Edited by Dr Adequate, : No reason given.