If we draw a line parallel to time axis from the point $(A)$ on graph at $t=0 \mathrm{sec}$. This line can intersect graph at $B$. In graph (b) for one value of displacement there are two different points of time. so, for one time, the average velocity is positive and for other time is equivalent negative.
As there are opposite velocities in the inteval 0 to $T$, hence average velocity can vanish in (b). This can be seen in the figure given below.
Here, $O A=B T$ (same displacement) for two different points of time.