If a Zed Shadow has Assault 4 and then gets swapped out and back in from Zed, does he get 8? Or does the Assault 4 not stack each time he attacks?

Yes, this works — the Assault stacks.

How it plays out:

1. First combat: The Shadow Clone attacks, triggering "When I attack." You banish a unit from trash, granting it Assault 4 this turn. Combat resolves.
2. Zed's swap: Zed, Without a Sound uses its activated ability — the Shadow Clone swaps places with Zed, leaving combat (losing Attacker designation). The Assault 4 effect persists until end of turn.
3. Second combat: The Shadow Clone attacks a different battlefield (or re-enters a new combat). It gains the Attacker designation in this new combat, so "When I attack" fires again. You banish another unit, granting Assault 4 a second time.

Per Rule 807.2, multiple grants of Assault sum their values — so that's Assault 4 + Assault 4 = Assault 8 while the Shadow is an attacker in the second combat.

A couple things to watch for:

• You need a unit in trash to banish for each trigger — that's two separate banishes.
• Each "When I attack" fires once per combat (FAQ #11693). Since these are two different combats, both triggers are valid.