y = 128x - 16x²
To find the maximum you want to differentiate the equation.
So,
dy/dx = 128 - 16*2x = 128 - 32x
You will then find the maximums and minimums when you put dy/dx = 0
So, 128 - 32x = 0
- 32x = - 128
x = (- 128)/(- 32)
x = 4
And by subtituting this value (x = 4) into the original equation we can find the value that y has when x = 4
So, y = 128x - 16x² = 128*4 - 16*(4)² = 512 - 256 = 256
So the equation is at a max at (4, 256)
[if it's required you can confirm that it is a max point by doing a table of signs. i.e. looking at whether dy/dx is bigger or smaller than zero before and after x = 4]