What is the keto form of a hexahydroxybenzene?
The question is badly phrased because it uses the term ‘the keto form’, implying that there be only one. In the case of hexahydroxybenzene, you are correct in that there is a monoketo form, at least two different diketo forms and potentially even more triketo forms.

All of these polyketo forms are created in the same way as the monoketo form except you do the isomerisation multiple times. So one way of arriving at the answer would be to check whether you can get to any of those molecules by tautomerising the hexahydroxy form often enough.

It may, however, be easier to think in the other direction, i.e. which ketones can I tautomerise to give a fully aromatic ring. Obviously, as your monoketo example shows, a ketone needs an &#x3b1;-hydrogen atom, so a) and b) cannot tautomerise at all and d) can tautomerise only twice, not three times. Upon careful examination of c) you should be able to realise that this can tautomerise three times to give hexahydroxybenzene.

Entirely out of scope of the textbook question is whether this tautomerisation is probable. None of the keto forms provides any advantage over the hexa-ol isomer in no solvent. We cannot argue with better hydrogen bonding and we cannot argue with polarity (both would favour the hexa-ol in all environments I can think of). Thus, the question in itself is somewhat academic. Yet it remains helpful to see how to get from polyketo to poly-ol forms and back.