Three comments:

1) The second answer you wrote is correct.

2) There is a negative sign missing in your first solution when you took the derivative of csc(x).

3) Some of your notation leaves something to be desired. In both solutions you wrote:

d/dx[3x^2] * d/dx[-4x^2] * y

to mean the result:

6x - 8xy

The actual result is:

d/dx[3x^2] * d/dx[-4x^2] * y = (6x)*(8x)*y = 48(x^2)y

You really need to write:

d/dx[3x^2] - d/dx[4x^2] * y

-Dan