Well, first, (x)(3x^2) is NOT 3x^4! It is 3x^3. It looks like you are using the "shell" method. Okay, then you are integrating

, the circumference of the circle the shell is rotated around, times the height of the shell. That is NOT 3x^2!

You want wine

**in** the glass, don't you? The interior of the glass is above the parabola. If the wine fills the glass to height "h" (and you see, I hope, that you are being asked how high to fill the glass). You should be integrating

. That will give the volume of wine in the glass. You want the glass filled to 45% of capacity. So you need to know "capacity". When x= 2, y= 3(2^2)= 12 so the full glass has volumne

. Calculate that, take 45% of it, set it equal to your previous integral and solve for h.