When vinyl flooring is damaged, the only way to repair it, without completely replacing it, is to patch it. For the best match, the patch should come from the same lot of material, so scrap leftovers from installation are a big help.
Find a repeating pattern in the print you can cut around to remove the damaged piece. Use a flat straight edge and keep your utility knife vertical while cutting. Then cut a repair piece from the scrap material so that it fits perfectly in the hole.
Vinyl glue on the subfloor will hold the patch, but you’ll need to clean up any excess with some mineral spirits.
Once the repair is dry, you’ll want to apply a seam sealer. And if you’ve done it right, the patch will be almost invisible.