A projectile is thrown upward so that it's distance above the ground after t seconds is h=-16t^2 + 672t. After how many seconds does it reach its maximum height?

It will reach its maximum height at the vertex of the parabola. Which is always:

(-b / (2a), (4ac-b^2) / (4a))

So the time when this occurs is the x coordinate, or t in this case.

-b / (2a), and b=672 and a=-16 so

t=-672/-32

t=21 seconds