On your way to class, you leave home and walk at 3 m/s east towards campus.
After one minute, and after covering 180 m, you realize that you left your physics assignment at home, so you turn around and run, at 6 m/s, back to get it. You're running twice as fast as you walked, so it takes 30 seconds to get home again.
For the 90 second out-and-back trip, what is your average speed?
The average speed is the total distance covered divided by the total time.
That works out to 360 m / 90 s = 4 m/s
What is your average velocity?
Average velocity is the net displacement divided by the total time.
Since the net displacement is zero, vavg = 0.