a boy sledding down a hill accelerates at 2.4 miles per second squared. if he starts from rest, in what distance would he reach a speed of 8.0 miles per second?

I think you have misread or mistyped the problem. "Miles" should be "Meters"

At 8 miles per second, he could launch himself into orbit!

When a*t = 8.0 m/s

Solve for t.
a = 2.4 meters/second^2
t = 3.33 seconds
The distance traveled to reach that speed is

d = (1/2)a t^2 = 13.3 meters