Given $(p\to q)\to r$ is false. It is possible only when $r$ is FALSE and $(p\to q)$ is TRUE.
Now even without checking any other option we can directly conclude option $D$ is correct as $(r\to p)\to q$ can be written as $\neg(r\to p)\vee q.$
Since, $r$ is False, $r\to p$ is true and $\neg (r\to p)$ is False. So, it becomes $(\text{False} \vee q).$
which is TRUE whenever $q$ is TRUE
Hence, option (D)