Say a ship leaves Earth traveling half the speed of light, but it carries a communication device that can communicate with Earth “instantaneously” (i.e., faster than light). From Earth’s frame of reference, time on board the ship is slowed down by a factor of 0.866, while from the ship’s frame of reference, time on Earth is slowed down by the same factor. (This isn’t some trick of perception—the geometry of spacetime distorts in such a way as to make both these observations true simultaneously.)
Now suppose a year has passed on Earth, and we use the device to communicate with the ship ”instantaneously”. From Earth’s frame of reference, the ship has currently experienced only 316 days of elapsed time, so that’s when they receive the signal according to their clock. But from their frame of reference, Earth at that point has only experienced 274 days of elapsed time—so when they send their “instantaneous” reply, it arrives on Earth three months before the original signal was sent.