What is 8 times 9 in 12-hour clock arithmetic? What is $8\times 9$ in $12$ hour arithmetic?
Will it be $0$, or will it be $6$?
$8*9 = 72$ and $72/12 = 6$
So is the answer $0$ or $6$?

Modular arithmetic deals with remainders upon division.  The remainder of $72$ upon dividing by $12$ is $0$.  So we have
$$8\cdot9\equiv72\equiv0\operatorname{mod}12$$
