The difference between the wrong answer and the correct one is $432$, whose ones digit is $2$. That means Judy writes neither $2$ nor $3$ wrong.  Compare $7\times63$ and $6\times72$, and we can get the correct answer.  $69\times72-63\times72=432.$ 
When calculating $63\times72$ , Judy fails to write the correct column multiplication. She writes one of the four digits as $9$ and gets a result which has a difference of $432$ from the correct one. Which digit does she write incorrectly? 

1. $$2$$ 
2. $$3$$ 
3. $$6$$ 
4. $$7$$ 
5. It\textquotesingle s impossible to determine. 