Average velocity is defined as
[tex]v_{mean} = \frac{displacement}{time}[/tex]
here for the whole trip we know that
[tex]displacement = 0[/tex]
so
[tex]v_{mean} = 0[/tex]
now for the average speed we can say
[tex]v_{mean} = \frac{distance}{time}[/tex]
here total distance is given as
[tex]d = 100 miles + 100 miles = 200 miles[/tex]
[tex]t = 2 + 4 + 2 = 8 hours[/tex]
now the average speed is given as
[tex]v_{mean} = \frac{200}{8} = 25 mph[/tex]
so this is the mean speed