You run 18 laps in 9 minutes. your friend runs 24 laps in 6 minutes. are the rates equivalent?

No, they are not equivalent.

In order to find the rates, take the number of laps, in this case, 18, and divide by the time, in this case, 9 minutes. 18/9=2. So, you run 2 laps every minute.
For the other rate, your friend's, do the same. Take 24 and divide by 6. 24/6=4. So, your friend runs 4 laps every minute.

Your friend is faster, and the rates are not equivalent.