Distance travelled by the particle cannot be zero when displacement is not zero.

Distance is the actual length of the path covered by a moving body irrespective of the direction in which body trace.

When a body moves from one position to another, then shortest (straight line) distance between initial and final positions of the body along with direction is displacement.

The above mentioned relation implies that the distance is always greater than or equal to displacement.

Hence, if 0, then Distance 0