In a multiplayer game, if an opponent's triggered ability and your triggered ability both trigger simultaneously, whose goes on the stack first?

When multiple triggered abilities trigger at the same time, the order they are placed on the stack is determined by the Active Player, Non-Active Player (APNAP) rule, found in CR 101.4 and CR 603.3b. First, the active player (whose turn it is) puts all of their triggered abilities on the stack in whatever order they choose. Then each other player, in turn order starting from the active player's left, does the same.

Because the stack resolves last-in, first-out, the abilities placed on the stack last will resolve first. This means the non-active player's triggers — placed on the stack after the active player's — will generally resolve before the active player's triggers.

If it is your opponent's turn (they are the active player), their triggers go on the stack first, and then yours go on top. Your triggers will therefore resolve first. If it is your turn, the reverse applies: your triggers go on first, your opponent's go on top, and your opponent's resolve first.

Concrete example: It's your opponent's turn. Both you and your opponent have a creature with a triggered ability that triggers when a land enters the battlefield. Your opponent plays a land. Under APNAP order, your opponent (active player) puts their trigger on the stack first, then you put yours on top. Your trigger resolves first, then your opponent's.

In a multiplayer game with more than two players, all non-active players place their triggers on the stack in clockwise turn order after the active player, so the last non-active player in turn order has their triggers on top and resolving first (CR 603.3b).