Let y = (x + 4) / (x - 2)
y'
= [(x - 2) d/dx (x + 4) - (x + 4) d/dx (x - 2)] / (x - 2)^2
= [(x - 2)(1) - (x + 4)(1)] / (x - 2)^2
= [(x - 2) - (x + 4)] / (x - 2)^2
= [x - 2 - x - 4] / (x - 2)^2
= -6 / (x - 2)^2
Hence, you were slightly wrong, though this could result in a huge marks loss.
Note that for any function of the form y = u / v, the derivative will be [v (du/dx) - u (dv/dx)] v^2