The easiest way to remove permanent marker from plastic is with a dry erase marker. The solvent in a dry erase marker can dissolve permanent marker ink.
Another way to remove permanent marker from plastic surfaces is to make a paste of baking soda and vinegar and leave the mixture on the marked surface for a few minutes. Rubbing toothpaste on the marker ink may also be effective because of the abrasive in the toothpaste. Bengay contains alcohol, which can remove marker ink. Sprinkling coffee grounds and then buffing the marked surface also works. Other household items that can remove permanent marker ink include peroxide, hand sanitizer, WD-40, Bar Keepers Friend cleanser and rubbing alcohol.