Two groups went hiking, leaving at the same time and arriving back at the same time. while one group moved away at the speed 6 mph and then moved back at the speed 4 mph, the other group moved all the way with the same speed. what was the speed of this second group, if both groups covered the same total distance, 24 miles?

This uses the formula d = r * t
First group

This group determines the time to be used by both groups.
t = d/r
t = 24 / 6
t = 4 hours hours going there.

t = 24 / 4
t = 6 hours 
Total time taken is 6 hours + 4 hours = 10 hours.

Group two

t = 10 hours.
d = 48 miles (remember, they have to come back).
r = 48 miles / 10 hours
r = 4.8 miles / hour
For humans, that actually is quite quick.