Plug the given initial speed and height into h(t).
h(t) = -16t2 + 15t + 6.5
It hits the ground when h(t) = 0. Use the quadratic formula to solve h(t) = 0. You will get a positive and a negative value. Since time starts at t = 0, the correct solution is the positive value.
Maximum height is reached at the vertex of the height-vs.-time parabola, which occurs at
t = -b/(2a)
a = -16
b = 15
Plug in the numbers and get t.
Evaluate h(t) at the time found in part (3).