My dog has had this white thing in its eye for many days and it can move. What’s going on?

Hello. From just this one photo I can’t pinpoint the eye problem, but it may be prolapsed lower-eyelid tissue. This is usually from inflammation or injury and can be treated with eye drops.

If you can, take the dog to a vet first to confirm the cause. If that’s not convenient right now, try eye drops and watch for improvement. If it doesn’t improve or gets worse, see a vet as soon as possible.