When you claim this expedition, deal 1 damage to each crew your opponents control.
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Explained
When you claim this expedition, deal 1 damage to each crew your opponents control.706.6, 301.7
It happens for the player who claims it, whoever launched it, and at once: claims happen in the battle step, after the crew destroyed there are gone (706.6). Each of your opponent's crew takes the damage, in their berth or dispatched; there is nothing to choose. Plating takes it first, the damage stays, and a crew left with no hull is destroyed once all of them have taken it. Their bases and your own crew aren't hit (705.7j).
Distance 6 · Spoils 2304, 706
Crew dispatched here on their own turn make progress, whoever launched it; on the opponent's turn they can only fight (706.3a). The first player to reach 6 progress claims it and gains 2 spoils.