WLOG $0$ is red.
Consider $1,3,5$ can't be all green, so at least one is red. WLOG $1$ is red.
Consider $2,4,6$ can't be all green, but $2,6$ can't be red, so $4$ is red.
So, $2,3,5,6$ must be green.
Now $9$ can't be red and can't be green, a contradiction!