I managed to do the first part okay ---- said some stuff about 3x^2 and y^2 term, its not linear etc..

but Im stuck in the part in red. Is it supposed to be something about a normal vector? How do i know what is wrong? and what mistake was made?

I calculated the equation of the tangent plane and it is: z=12(x−2)−6(y−3)-1

and the tangent plane has normal vector (12,-6,-1) at (2,3) ----- could it be something to do with the part circled in red?