Consider the distance versus time plot for the movement of particle from A and B as shown below.
Now, the average velocity is, Average velocity=
Total displacement from A to B
Total time interval
Since, the total displacement depends on straight distance between the initial and final points. Hence, displacement between A and B is always non zero.Therefore, the average speed is always non zero, but no distance is travelled between point C to D. So instantaneous speed at every instant between point C to D is zero.Thus, the average speed is always non zero and instantaneous speed can be zero.