It's a standard setup. You must know only these:
a(t) = -g -- g is acceleration due to gravity
v(t) = -g*t + v0 -- v0 is the initial velocity that we are not given.
s(t) = -½g*t^2 + v0*t + h0 -- h- is the initial height that we are given.
s(t) = -½g*t^2 + v0*t + 16 m
It hits the ground when? s(t) = 0
0 = -½g*t^2 + v0*t + 16 m
This gives the slightly untidy .
There's another solution, but it's negative and I'm sure we don't want that.
We are given the velocity on impact.
That should lead you to the initial velocity. (Hint: I get a little over 19 m/s)
Once you have that, you are on your way to a simple solution of the maximum of a parabola.