To understand this problem, it helps to think of a familiar concept first. Let's take driving for example:
So your car is moving at 40mph or 40 miles per hour.
Your unit rate is miles per hour. If you break that down you have distance per time.
Another way of writing miles per hour is miles/hour. The "per" part translates to the / symbol.
If you take your question, you can see that you have similar units of distance (3/8 meters) and time (6 minutes).
So then your unit rate here will be meters per minute or m/min