Repeat the following process X times. Each opponent loses 3 life unless that player sacrifices a nonland permanent or discards a card.
7/14/2017 If X is 0, Torment of Hailfire resolves with no effect.
7/14/2017 While resolving Torment of Hailfire, your opponent chooses a card to be discarded without revealing it, chooses a nonland permanent to be sacrificed, or chooses to do neither. Then that player discards that card, sacrifices that permanent, or loses 3 life, then repeats this process if it hasn’t been done X times yet. Your opponent can always choose to lose 3 life, even if they have cards to discard or nonland permanents to sacrifice.
7/14/2017 Each repetition through this process is done separately. If an opponent sacrifices a creature with an ability that triggers when another creature dies, for example, it will see creatures that are sacrificed before it, but not those are sacrificed after it.
7/14/2017 State-based actions aren’t checked in between repetitions of this process, so the game state may be a little unusual while making the choice. For example, a player may sacrifice a creature and then later sacrifice an Aura that was attached to that creature.
7/14/2017 In a multiplayer game, each opponent in turn order makes their choice once, then all of the actions occur simultaneously, then they repeat this process if it hasn’t been done X times yet. Opponents will know choices made by earlier opponents when making their choices, although a card chosen to be discarded this way isn’t revealed until it’s discarded.
7/14/2017 In a Two-Headed Giant game, Torment of Hailfire causes both opponents to sacrifice a nonland permanent, discard a card, or lose 3 life X times. Your opponents can choose the same torment or different ones each time.