Wondrous Creatures · Board game rules
When can Throboros/Throiamet's ability be used?
Quick answer
Throboros/Throiamet's ability can be used any time you use an Energy on it, but only immediately after you discard a card costing 3 resources or less — it then lets you play that discarded card for free.
Details
When Throboros (or its twin, Throiamet) is played, you immediately take 1 Energy from the Supply and place it on the card [p.31 — CREATURE CARDS]. Using an Energy is a Free Action, so it can be triggered at any time during your turn [p.18 — V. FREE ACTIONS]. However, the ability itself only functions if you have "just discarded a card with a cost of 3 resources or less" — you then discard the Energy from Throboros to play that discarded card to your reserve without paying its cost [p.31 — CREATURE CARDS].
Because playing the card this way is the result of using an Energy (a Free Action), it does not consume your Basic Action [p.31 — CREATURE CARDS]. The rulebook gives an example where, during a Recharge Action, you discard an excess card (e.g., Rockin, costing 2 resources) to meet the 5-card hand limit, then immediately use Throboros's Energy to bring that card back and play it for free [p.31 — CREATURE CARDS].
Watch out: When checking whether a card's cost is 3 resources or less, you must use its initial printed cost, not any discounted cost from other abilities. For example, Cavigator's initial cost is 4 resources, so it can never be played via Throboros/Throiamet even if a discount would lower it below 3 [p.31 — CREATURE CARDS]. Also, since each card's Energy can only be used once per turn, you can only trigger this ability once per turn per copy of Throboros/Throiamet in your reserve [p.18 — V. FREE ACTIONS].