Nomenclature priority of prefixes consisting of identical letters but containing different locants
The compound that is given in the question consists of a cyclohexane ring with two substituent groups: 1-chloroethyl and 2-chloroethyl.

The correct numbering of locants is stipulated by Rule 14.4 in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book): 


  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:
  (…)


However, the given case is not explicitly mentioned in this rule.

The correct numbering is actually indirectly given by Rule 14.4 (g):


  (g) lowest locants for the substituent cited first as a prefix in the name;


Since the correct order of citation as a prefix in the name is given by Rule P-14.5.4:


  P-14.5.4 When two or more prefixes consist of identical Roman letters, priority for order of citation is given to the group that contains the lowest locant(s) at the first point of difference.


Thus, ‘1-chloroethyl’ is cited before ‘2-chloroethyl’ in the name, and thus a low locant is assigned first to the 1-chloroethyl group.

Therefore, the complete name for the compound that is given in the question is 1-(1-chloroethyl)-4-(2-chloroethyl)cyclohexane.