h(t)=0 when the projectile falls to the ground so -16t²+32t+48=0.
If we divide through by -16 we get t²-2t-3=0=(t-3)(t+1) when factorised.
So either t-3=0 or t+1=0. The only positive solution is t=3 seconds, so it takes 3 seconds to fall to the ground.