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.

So,

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.