Exile target artifact, creature, or enchantment an opponent controls. That player may put a permanent card from their hand onto the battlefield.
A permanent card is an artifact, creature, enchantment, land, or planeswalker card.
If the artifact, creature, or enchantment is an illegal target as Divine Gambit tries to resolve, Divine Gambit won't resolve and none of its effects will happen. No player will put any cards onto the battlefield.
If the player chooses to put a double-faced card onto the battlefield, it enters with its front face up. They may do this only if the front face of the card is a permanent card.