Question

In what condition is the distance covered equal to the magnitude of the displacement of a particle

Answer 1

As we know the displacement is the shortest distance between the initial and final positions.
And the distance is the length of the actual path.
 
            If the object travels in the straight path the length of the actual path and the shortest distance are same. So the distance and the displacement are equal to each other if the object travels in the straight path

Answer 2

if the path is a straight line then and only then it is possible!