As an additional cost to
castTo cast a spell is to take it from the zone it’s in (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. A player may cast a spell if they have priority. See rule 601, “Casting Spells.”
To cast a card is to cast it as a spell. (CR 701.5) this spell,
exileTo exile an object, move it to the exile zone from wherever it is. See rule 406, “Exile.” (CR 701.13) an instant or sorcery card from your graveyard.
Draconic Intervention deals X damage to each non-Dragon creature, where X is the exiled card's mana value. If a creature dealt damage this way would die this turn,
exileTo exile an object, move it to the exile zone from wherever it is. See rule 406, “Exile.” (CR 701.13) it instead.
ExileTo exile an object, move it to the exile zone from wherever it is. See rule 406, “Exile.” (CR 701.13) Draconic Intervention.