The ratio of speed of $3$ cars are $3:4:6$. What is the ratio of time taken by these cars to cover the same distance?

Since distance is constant, speed ($S$) is inversely proportional to time ($T$):
$$T\propto \frac{1}{S}$$

Given the speed ratio $S_1:S_2:S_3=3:4:6$, the time ratio will be:

$$T_1:T_2:T_3=\frac{1}{3}:\frac{1}{4}:\frac{1}{6}$$

To simplify, multiply by the $\text{LCM}$ of $3,4,\text{ and }6$, which is $12$:

$$T_1:T_2:T_3=\left(\frac{1}{3}\times 12\right):\left(\frac{1}{4}\times 12\right):\left(\frac{1}{6}\times 12\right)=4:3:2$$