The y-intercept is when x=0, so it's -24. When y=f(x)=0. -2x^3+26x-24=0. By inspection putting x=1, we have f(1)=-2+26-24=0, so x=1 is a zero and (x-1) a factor. The equation can also be written x^3-13x+12=0. Using synthetic division we can find out the other factor, which is x^2+x-12=0=(x+4)(x-3), so the other zeroes are -4 and 3. Therefore the x-intercepts are -4, 1 and 3.