Remember that it is not he who reviles you or strikes you, who insults you, but it is your opinion about these things as being insulting. When then a man irritates you, you must know that it is your own opinion which has irritated you. Therefore especially try not to be carried away by the appearance. For if you once gain time and delay, you will more easily master yourself.
The last sentence is the actionable part. The interval between impression and assent is where the work is done — what the Stoics called prosochē, sustained attention. Gain time. Delay. Wait long enough for the appearance to lose its imperious quality, and the choice to assent or refuse becomes available again. The Stoics return to this gap constantly; it is the only door through which freedom enters.
Epictetus, Enchiridion 20 · trans. George Long (1877)
Context
The point is procedural, not merely consoling. Epictetus's claim: the other person's words are out there in the air. The injury is your judgment that those words are damaging. Eliminate the judgment, and the injury is eliminated at its source — not by suppression but by accurate location of where it lives.