How to name the tautomers of hexane-2,4-dione correctly according to IUPAC rules?
You numbered all locants together in a series and you found the lowest set of locants according to Subsection P-14.3.5 of the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) since the locant set ‘2,2,4’ is lower than ‘3,4,5’.


  P-14.3.5 Lowest set of locants
  
  The lowest set of locants is defined as the set that, when compared term by term with
  other locant sets, each cited in order of increasing value, has the lowest term at the first
  point of difference; (…)


This approach would be correct if all locants refer to detachable prefixes (like ‘2-hydroxy’). However, in the given compounds, the locants refer to prefixes (‘hydroxy’), endings (‘ene’), and suffixes (‘one’). The assignment of low locants to such different features is stipulated in Subsection P-14.4 as follows:


  P-14.4 NUMBERING
  
  When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
  
  (…)
  
  (c) principal characteristic groups and free valences (suffixes);
  
  (…)
  
  (e) saturation/unsaturation:
  
    (i) low locants are given to hydro/dehydro prefixes (…) and ‘ene’ and ‘yne’ endings;
  
    (ii) low locants are given first to multiple bonds as a set and then to double bonds (…);
  
  (f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;
  
  (…)


Therefore, the resulting name is (4​Z)-5-hydroxyhex-4-en-3-one (not (2​Z)-2-hydroxyhex-2-en-4-one) since the locant ‘3-one’ for the principal characteristic groups is lower than ‘4-one’.