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Rulings
If the back face of a modal double-faced card is countered, you will not be able to exile any cards, including the one that you countered, because those cards have only their front-face characteristics (including name) in the graveyard, hand, and library.
Countering a spell normally puts that card into the graveyard, so that card will be there to find and exile.
Countering a spell normally puts that card into the graveyard, so that card will be there to find and exile.
Rulings
If the back face of a modal double-faced card is countered, you will not be able to exile any cards, including the one that you countered, because those cards have only their front-face characteristics (including name) in the graveyard, hand, and library.
Countering a spell normally puts that card into the graveyard, so that card will be there to find and exile.
Countering a spell normally puts that card into the graveyard, so that card will be there to find and exile.
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