We want h > 192, so ...
-16t^2 +128t > 192
t^2 -8t < -12 . . . . . . . divide by -16
t^2 -8t +12 < 0 . . . . . add 12
(t -6)(t -2) < 0 . . . . . . factor
The zeros of this are t=2 and t=6. The signs of the factors will be different, hence their product will be negative, for values of t between these zeros.
The projectile's height exceeds 192 feet in the interval 2 < t < 6.
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