Your basic equation is

    h(t) = -16t^2 + 32t + 48.



The projectile will hit the ground when h(t) = 0.



Thus the equation to solve is

    -16t^2 + 32t + 48 = 0.    (1)


You can simplify this equation SIGNIFICANTLY dividing both sides by -16. 

You will get an EQUIVALENT equation

    t^2 - 2t - 3 = 0.    (2)


The term "EQUIVALENT" means that it has the same roots as equation (1).


Now you can factor equation (2) easily  (and MENTALLY)

    (t-3)*(t+1) = 0.


The roots are  t= 3  and  t= -1, and only  positive root t= 3 is meaningful.


ANSWER.  The projectile will hit the ground in 3 seconds.