One-fourth of the distance between two cities is 100 kilometers less than two-thirds the distance between the cities. Which equation expresses this situation?

Let $d$ represent the distance between the two cities in kilometers.

"One-fourth of the distance between two cities" can be written as $\frac{1}{4}d$.
"two-thirds the distance between the cities" can be written as $\frac{2}{3}d$.
The phrase "is 100 kilometers less than" means that $\frac{1}{4}d$ is equal to $\frac{2}{3}d$ minus 100.

So, the equation is:

The equation $\frac{1}{4}d = \frac{2}{3}d - 100$ matches option C.

The final answer is $\text{C. } \frac{1}{4}d = \frac{2}{3}d - 100$.