If I am attacking a battlefield with a 6 might vs a 6 might and pass focus, they end the showdown, can I play a reaction?

No, you cannot play a reaction after both players have passed focus in a showdown.

According to RiftJudge FAQ #7747 and Rule 348.1, once both players pass focus in succession, the showdown ends. If it is a combat showdown, the game proceeds directly to the combat damage step, where no player has priority to play spells or activate abilities.

The Sequence

1. Attacker has Focus/Priority: You choose to Pass.
2. Defender has Focus/Priority: They choose to Pass.
3. Showdown Closes: Because both players passed consecutively, the showdown ends immediately (Rule 348).
4. Combat Damage Step: The game moves directly into assigning and dealing damage (Rule 460).

There is no "reaction window" between the final pass and the assignment of combat damage.

Important Note: As long as the showdown is open, you are free to play reactions while you have priority. However, once you pass focus, you are choosing to exit the window of opportunity to act. If your opponent plays an item after you pass, you will regain priority and have a new opportunity to play a reaction before that specific item resolves (as described in RiftJudge FAQ #10660), but you cannot retroactively play a reaction once both players have passed and closed the showdown.