jmc

The largest power of 6 less than 515 is $6^3=216$, and the largest multiple of 216 less than 515 is $2\cdot 216=432$. That means there is a 2 in the $6^3$ place. We have $515-432=83$ left. The largest multiple of a power of 6 that is less than 83 is $2\cdot 6^2=72$. There is a 2 in the $6^2$ place. Now we're left with $83-72=11$, which can be represented as $1\cdot 6^1+5\cdot 6^0$. So, we get $515=2\cdot 6^3+2\cdot 6^2+1\cdot 6^1+5\cdot 6^0=\boxed{2215_6}$.