Give one example of a situation in which a body has a certain average speed but its average velocity is zero.

When a body has completed one round around  a circular path. Its displacement would be zero.

Therefore, in this situation, the body will have a certain average speed but the certain average velocity would be zero.

For example, In the above fig. If a body completes a round from $A\rightarrow B\rightarrow B\rightarrow C\rightarrow A$ in time $t$.

Here displacement $d=0$

Therefore, average velocity $v=\frac{displace}{time}=\frac{d}{t}=\frac{0}{t}=0$

Let $r$ be the radius of the circular path. 

Then distance travelled by the body $s=2\pi r$

Therefore, average speed of the body$=\frac{distance}{time}=\frac{s}{t}$

$=\frac{2\pi r}{t}$