dy/dx=3x2-24x. At a turning point dy/dx=0 so 3x2-24x=0=3x(x-8), so x=0 and x=8 are turning points.
d2y/dx2=6x-24. If we put x=0 into this it evaluates to -24, a negative number, representing a maximum (concave down). When x=8 it's 24, a positive number, representing a minimum (concave up).