The answer would be: 128
You can find minimum value by looking at the vertex. First, differentiate the equation and find the value of x.
y=2x^2-32x+256
4x - 32=0
4x=32
x=8
If you put x=8, the value would be:
y=2x^2-32x+256
y=2(8)^2-32(8)+256
y= 128- 256 + 256= 128