When Rod of Absorption's last ability resolves, you cast as many spells with total mana value X or less from among the exiled cards as you would like in any order you choose. Cards not cast this way will remain in exile indefinitely.

If a spell is countered or it never resolves, Rod of Absorption will not exile it.

If the card has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

If multiple Rods of Absorption are on the battlefield at the same time, any player casting an instant or sorcery spell will cause all of them to trigger. As the spell resolves, its controller will choose which of the Rods gets to exile it.

Each Rod of Absorption tracks the cards it has exiled separately. If Rod of Absorption is destroyed and then later brought back to the battlefield, it will not be able to access any of the cards that it had exiled before.

If you cast a spell “without paying its mana cost,” you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, you must pay those to cast the spell.