I'm grateful for your post, but I think you made a mistake. Shouldn't it be ?
BTW, the answer is . I'm not sure where you went wrong with your method.
Here's what I did;
y' = 9(2-x^2)^2 (-2x)
y'' = 18(2-x^2)(-2x)(-2)
At this point I realized my method wasn't matching up to the given answer so I stopped. Could somebody tell me where I went wrong?