The vertical height in feet of a projectile on a planet in our solar system at a given time t in seconds is represented by the function h(t)=−6t2+24t. Re-write h(t) in the form \large h\left(t\right)=a\left(t-h\right)^2+k and determine the maximum height of the projectile.

So you want it in the form

h(t) = a(t - h)^2 + k , (why not just type it like this)

I will assume you are learning about completing the square ...

h(t) = -6t^2 + 24t
h(t) = -6(t^2 - 4t + 4) + 24 , (expand this to see that you get the original)
= -6(t - 2)^2 + 24

the max is 24 when t = 2