The speeds of three cars are in the ratio $2:3:4$. The ratio between the time taken by these cars to travel the same distance is:

We know that speed ($S$) is inversely proportional to time ($T$) when the distance ($D$) is constant:
$$T\propto \frac{1}{S}$$

Given the ratio of speeds of the three cars:

$$S_1:S_2:S_3=2:3:4$$

Therefore, the ratio of the time taken by them to cover the same distance will be:

$$T_1:T_2:T_3=\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$$

To convert this into a whole number ratio, multiply each term by the Least Common Multiple (LCM) of the denominators $(2,3,\text{ and }4)$, which is $12$:

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

$$T_1:T_2:T_3=6:4:3$$