..........t = ?
x0 = 0 m.......x = 25 m
v0 = ?..........v = 0 m/2 (since it has stopped)
..........a = -8 m/s^2
We want to know v0, so we need to know an equation for v0 that doesn't contain t. A good choice would be:
v^2 = v0^2 + 2a(x - x0)
0 = v0^2 +2(-8)(25 - 0) <-- Leaving the units out for convenience.
0 = v0^2 - 400
v0^2 = 400
v0 = (+/-) 20 m/s
Now, which sign do we choose? Since all we want is the speed, which is the magnitude of the velocity, we don't care. (For the record, the initial velocity is positive, since that's how we defined the positive direction in the first place.) So the greatest speed is 20 m/s.