jmc

Dividing 811 by 24 gives a quotient of 33, so the greatest multiple of 24 less than $-811$ is $24\cdot -34=-816$. Thus $-811$ is $-811-(-816)=5$ more than a multiple of $24$. Since $0\le 5<24$, the residue of $-811$ is $\boxed{5}$ (mod 24).