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On the previous slide, the first term is already axial symmetric. The second term is only axial symmetric if eta = 0, this is when Vxx == Vyy (which is the case when looking at the matrix). When looking at the toy model we see that there is rotation symmetry around at least one axis, this means there is axial symmetry. A toy model where Vxx is not equal to Vyy will have no axial symmetry. This is when there is a electrical distribution differentce between the x and y axes, for example if one of the electric charges would be more elongated towards the y axis.
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