The addition below is incorrect. What is the largest digit that can be changed to make the addition correct?
$\begin{tabular}{rr}&\ \texttt{6 4 1}\\ &\texttt{8 5 2}\\ &+\texttt{9 7 3}\\ \hline  &\texttt{2 4 5 6}\end{tabular}$
$\text{(A)}\ 4\qquad\text{(B)}\ 5\qquad\text{(C)}\ 6\qquad\text{(D)}\ 7\qquad\text{(E)}\ 8$
Doing the addition as is, we get $641 + 852 + 973 = 2466$.  This number is $10$ larger than the desired sum of $2456$.  Therefore, we must make one of the three numbers $10$ smaller.
We may either change $641 \rightarrow 631$, $852 \rightarrow 842$, or $973 \rightarrow 963$.  Either change results in a valid sum.  The largest digit that could be changed is thus the $7$ in the number $973$, and the answer is $\boxed{\textbf{(D) }7}$.