If the number of five digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to:

$\begin{array}{|lllll|}\hline & & & 2& \\ \hline\end{array}$

The first blank can be filled with any one of the digits 1,3,4,5,6,7,8,9 in 8 ways

The second blank can be filled with any one of the digits 0,1,3,…, without taking first digit, in 8 ways

The third blank can be filled with the remaining 7 digits in 7 ways 

And the unit place can be filled with the remaining 6 digits in 6 ways

Hence the number of numbers $=8\times 8\times 7\times 6=2688=336\cdot k\Rightarrow k=\boxed{8}$