In this case, the relevant criteria for the numbering are:
- lower locants for suffixes (here: ‘ol’)
- lower locants for multiple bonds (here: ‘yne’)
- lower locants for prefixes (here: ‘bromo’)
The corresponding subsection 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;
(…)
Therefore, the correct name for the compound given in the question is ‘7,7-dibromooct-5-yn-4-ol’ (not ‘2,2-dibromooct-3-yn-5-ol’) since the locant ‘4’ for the suffix ‘ol’ is lower than ‘5’.
