As the universe expands, light expands with it, redshifting the light. That’s the essence of Hubble’s Law. The older the light, the more its waves will be expanded (and its frequencies redshifted) by its journey through the expanding universe. So astronomers can look at a galaxy’s spectrum, find the emission and absorption peaks of different elements, see how much they’ve shifted, and then apply Hubble’s Law to that shift to figure out how far away that galaxy is.
For close objects, light “age” is known from a distance measurement, as Charyou-Tree said.
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