Two possible chains - isopropyl or ethyl and methyl?
The first important simplified criteria for the choice of a principal chain in such compounds are:


greater number of suffixes
longest chain
greater number of multiple bonds
lower locants for suffixes
lower locants for multiple bonds


The corresponding wording of the nomenclature rules (taken from Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book)) reads as follows:


  P-44.1 SENIORITY ORDER FOR PARENT STRUCTURES
  
  When there is a choice, the senior parent structure is chosen by applying the following criteria, in order, until a decision is reached. These criteria must always be applied before those applicable to rings and ring systems (see P-44.2) and to chains (see P-44.3). Then criteria applicable to both chains and rings or ring systems given in P-44.4 are considered.
  
  P-44.1.1 The senior parent structure has the maximum number of substituents corresponding to the principal characteristic group (suffix) or senior parent hydride in accord with the seniority of classes (P-41) and the seniority of suffixes (P-43).
  
  (…)
  
  P-44.3.2 The principal chain has the greater number of skeletal atoms [criterion (b) in P-44.3].
  
  (…)
  
  P-44.4.1 If the criteria of P-44.1 through P-44.3, where applicable, do not effect a choice of a senior parent structure, the following criteria are applied successively until there are no alternatives remaining. These criteria are illustrated in P-44.4.1.1 through P-44.4.1.12.
  
  The senior ring, ring system, or principal chain:
  
  (a) has the greater number of multiple bonds (P-44.4.1.1);
  
  (b) has the greater number of double bonds (P-44.4.1.2);
  
  (…)
  
  (h) has the lower locant for an attached group expressed as a suffix (P-44.4.1.8);
  
  (…)
  
  (j) has the lower locant(s) for endings or prefixes that express changes in the level of hydrogenation, i.e., for ‘ene’ and ‘yne’ endings and ‘hydro/dehydro’ prefixes (P-44.4.1.10);
  
  (…)


Since the compound that is given in the question does not have any principal characteristic group (a characteristic group chosen for citation at the end of a name by means of a suffix or a class name, or implied by a trivial name), the first criterion (greater number of suffixes) given in P-44.1.1 is not relevant in this case.

The second criterion given in P-44.3.2 is the longest chain. However, both possible names, (3⁠Z)-3-ethyl-2-methylhex-3-ene and (3⁠Z)-3-(propan-2-yl)hex-3-ene, indicate a principal chain with six skeletal atoms.

Also, both possible principal chains include the double bond. Therefore, the criteria given in P-44.4.1 (a) (greater number of multiple bonds) and (b) (greater number of double bonds) cannot be used to reach a decision.

The criterion given in P-44.4.1 (h) (lower locant for the suffix) is not relevant since the compound that is given in the question does not have any suffix.

Finally, the criterion given in P-44.4.1 (j) stipulates that the principal chain shall have the lower locant for the double bond, i.e., for the ‘ene’ ending. However, both names, (3⁠Z)-3-ethyl-2-methylhex-3-ene and (3⁠Z)-3-(propan-2-yl)hex-3-ene, have the locant 3 for the ‘ene’ ending.

Further criteria can be found in Section P-45:


  P-45 SELECTION OF PREFERRED IUPAC NAMES
  
  P-45.0 INTRODUCTION
  
  Two or more names may result based on the same senior parent structure selected according to P-44, because of different substitution patterns or multiple occurrences of the same senior parent structure. (…) Application of
  the criteria in this section will generate the preferred IUPAC name.
  
  (…)
  
  P-45.2.1 The preferred IUPAC name is based on the senior parent structure that has the maximum number of substituents cited as prefixes (other than ‘hydro/dehydro’) to the parent structure.
  
  (…)


In accordance with P-45.2.1, the preferred principal chain corresponds to (3⁠Z)-3-ethyl-2-methylhex-3-ene, which has a principal chain with two substituents (3-ethyl, and 2-methyl), whereas the principal chain of (3⁠Z)-3-(propan-2-yl)hex-3-ene has only one substituent (3-(propan-2-yl)).