What should be the name of the given compound?
The most important simplified criteria for the numbering in such cases are:

lower locants for the principal characteristic group that is expressed as suffix
lower locants for multiple bonds
lower locants for prefixes
lower locants for substituents cited first as a prefix in the name

The corresponding actual wording in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads 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;
(g) lowest locants for the substituent cited first as a prefix in the name;
(…)

For the compound that is given in the question, the principal characteristic group is $\ce{-OH}$. It is expressed as suffix “ol”. Thus, low locants are assigned first to the $\ce{-OH}$ groups according to Rule (c), which yields “…1,3-diol”.
Next, a low locant is given to the double bond according to Rule (e), which gives “4-ene-1,3-diol”.
This step also establishes the numbering of the other atoms of the ring so that there is no longer a choice for the last substituent. Nevertheless, strictly following the rules, a low locant can be assigned to the remaining substituent according to Rule (f).
Thus, the complete name is 6-sulfanylcyclohex-4-ene-1,3-diol. Note that the prefix “mercapto” is no longer recommended.