When you are challenged by another player, there are two possible outcomes: either you win, or the challenger wins.

You win the challenge

You win if you reveal the relevant card in front of you. Return your revealed card to the deck, shuffle the deck, and then draw a random replacement card (look at it, then place it face-down in front of you). Then go ahead with the action or counter-action as normal.

The player who loses the challenge must choose one of their cards to lose (turn it face-up for the rest of the game). If that is their last card, they are out of the game.

The challenger wins the challenge

The other player wins the challenge if you can't or don't want to reveal the relevant card. Your entire action then fails, so you don't have to spend the coins that the action would have cost you. Your turn ends.

The player who loses the challenge must choose one of their cards to lose (turn it face-up for the rest of the game). If that is their last card, they are out of the game.