, 2013

Solution:

We can rewrite this as $(10 \times 2)(13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1) = (10^3)(2 \times 13 \times 12 \times 11 \times 9 \times 8 \times 7 \times 6 \times 4 \times 3)$. Multiplying together the units digits for the terms not equal to $10$ reveals that the rightmost non-zero digit is $6$.