The difference between the wrong answer and the correct one is $1920$, whose ones digit is $0$. That means Judy writes neither $4$ nor $6$ wrong. Then, compare $20\times54$ and $20\times96$, so we can get the correct answer. $74\times96-54\times96=1920.$ 
When calculating $54\times 96$, Judy fails to write the correct column multiplication. She writes one of the four digits as $7$ and gets a result which has a difference of $1920$ from the correct one. Which digit does she write incorrectly? 
Options:
$$5$$ 
$$4$$ 
$$9$$ 
$$6$$ 
It\textquotesingle s impossible to determine. 