Someone . if you could possibly show your work or tell me what you did that would be wonderful.

Start by getting all of your stuff on the same side.
(4x^2 - 1)/2y - (9y - 5)/3 - z+3y = 0

Then, move the (4x^2 - 1)/2y to the other side of the equation by subtracting it from both sides.
- (9y - 5)/3 - z+3y  = -(4x^2 - 1)/2y

Next, get all your ys on the same side of the equation. To do this, multiply both sides by 2y.
2y * (- (9y - 5)/3 - z+3y ) = -(4x^2 - 1)

Simplify this out.
(-18y^2 - 10y)/3 - 2yz +6y^2 = -(4x^2 - 1)

(-18y^2 - 10y)/3 is equal to  -6y^2 - 10y/3, so the equation can be rewritten as
-6y^2 - 10y/3 - 2yz +6y^2 = -(4x^2 - 1)
The 6y^2 and -6y^2 cancel eachother out and equal zero.
- 10y/3 - 2yz  + 0 = -(4x^2 - 1)

Now we have to move z over. To do this, factor out a y from each term.
y(-10/3 - 2z) =  -(4x^2 - 1)

Now, all we have to do is divide both sides by (-10/3 - 2z) to get
y = -(4x^2 - 1)/(-10/3 - 2z)

If we simplify this out, we will find that it is equal to
y = -3(4x^2 - 1)/(-10 - 6z)  = -3(4x^2 - 1)/-2(5 + 3z) = 3(4x^2 - 1)/2(5 + 3z)
y = 3(4x^2 - 1)/2(3z + 5)

The answer is D.