Question

when is the distance and the displacement of an object equal?

Answer 1

Distance is the length between the initial point and the final point. It doesn't take into consideration the direction in which your travelling. For example: If you travel from point a to point b, 20m apart and point b to point c, 30m apart, the total distance travelled by you will be 50m 
As for the case of displacement,  it is the shortest distance between the initial point and the final point I.e a straight line and it takes into consideration your direction of travelling. 
So if you travel in a straight path, then your distance will be equal to your displacement... 

Answer 2

distance and displacement can be equal because displacement is the distance from the origin while distance is the total length travelled.