Does the substituent that comes alphabetically first take precedence, or do we look for the next nearest substituent, or is it a combination of both?
The substituents in the compound that is given in the questions are not equidistant from both ends.
Numbering from left to right yields the name 5-bromo-3-chloro-7,8-diethyl-2,9-dimethyldecane (i.e. the locant set ‘2,3,5,7,8,9’), whereas numbering from right to left yields the name 6-bromo-8-chloro-3,4-diethyl-2,9-dimethyldecane (i.e. the locant set ‘2,3,4,6,8,9’).
Concerning numbering, the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:
When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
(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;
Note that Rule f takes precedence over Rule g.
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; (…)
Therefore, the example is named as 6-bromo-8-chloro-3,4-diethyl-2,9-dimethyldecane rather than 5-bromo-3-chloro-7,8-diethyl-2,9-dimethyldecane since the locant set ‘2,3,4,6,8,9’ is lower than ‘2,3,5,7,8,9’.