how do deal 4 damage with red akali

A single Akali, Deadly Weapon move trigger caps at 1 damage (2 if Empowered), so 4 means either two triggers or Bonus Damage on one.

Two triggers (the usual route): Empower her ([2][C], so she deals 2 instead of 1), Move her to a battlefield, then as a Reaction to her "When I move" trigger play Flash to move her back to base. Each move creates its own trigger — 2 + 2 = 4 to the same unit. Because the chain never empties, no Showdown ever opens, so there's no Combat Cleanup and the damage isn't healed (FAQ #11658). If instead you pull her back with the Rogue Assassin legend, the Combat Showdown has already started, so that damage gets healed at Combat Cleanup unless it was lethal.

Bonus Damage: Annie, Fiery ("your spells and abilities deal 1 Bonus Damage") turns an Empowered trigger into 3, Rabadon's Deathcrown attached makes it 5, and Void Gate battlefield adds 1 to units there — Bonus Damage applies per instance of the deal action (Rule 715.1), so it stacks on top of either route.