Question 368649
You have it factored right...Set equal to 0 to find x values (there will be 2)

0=-8x(2x-3)
-8x=0  2x-3=0
x=0 and x=3/2  These are the y intercepts and we know from the function that it is an upside down parabola. (because of the -16x^2)  

To find the maximum point (which would be the vertex) take the derivative of the function
y=-16x^2+24x
y'=-32x+24    Set equal to 0 and solve for x
-32x+24=0
x=3/4  Plug x=3/4 back into the original function

y=-16(3/4)^2+24(3/4)  Solve for y

y=-9+18=9.  So your vertex is at the point (3/4,9)