In the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), the order of citation of substituent prefixes and the numbering of the corresponding locants are laid down in two different rules.
Simple substituent groups that are named by means of prefixes (such as ‘methyl’ and ‘ethyl’) are arranged alphabetically.
P-14.5 ALPHANUMERICAL ORDER
Alphanumerical order has been commonly called ‘alphabetical order’. As these ordering principles do involve ordering both letters and numbers, in a strict sense, it is best called ‘alphanumerical order’ in order to convey the message that both letters and numbers are involved
Alphanumerical order is used to establish the order of citation of detachable substituent prefixes (not the detachable saturation prefixes, hydro and dehydro), and the numbering of a chain, ring, or ring system when a choice is possible.
P-14.5.1 Simple prefixes (i.e., those describing atoms and unsubstituted substituents) are arranged alphabetically; multiplicative prefixes, if necessary, are then inserted and do not alter the alphabetical order already established.
Therefore, the correct alphanumerical order for the compound given in the question is x-ethyl-y,y-dimethylcyclooctane (not x,x-dimethyl-y-ethylcyclooctane).
The locants x and y are used to indicate positions of the parent structure at which modifications represented by suffixes occur. The relevant rules concerning the numbering of locants for substituent prefixes are:
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; (…)
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).
In accordance with Rule (f), the compound given in the question is named as 5-ethyl-1,1-dimethylcyclooctane, not 1-ethyl-5,5-dimethylcyclooctane since the locant set ‘1,1,5’ is lower than ‘1,5,5’. And thus, Rule (g) is not required in this case.