First, by # 4149, its unit digit cannot be odd. Therefore, $N$ must be even. It follows that its unit digit can only be $0$, $4$, or $6$.

Next, because $N$ is even, then $N\equiv 0\pmod{4}$ must hold. It is now easy to verify only $6$ is possible when the tens digit is odd because none of $10$, $30$, $\cdots$, and $14$, $34$, $\cdots$ is a multiple of $4$.