Is preference given to long alkyl group or branched cycloalkane?
According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), two methods are possible for naming systems composed of rings and chains: either the ring or the chain can have seniority. To construct the preferred IUPAC name (PIN), the ring is selected as the parent structure.


  P-44.1.2.2 Systems composed of rings and chains (exclusive of linear phanes)
  
  Two methods are recognized to name systems composed of rings and chains
  (exclusive of linear phanes).
  
  (1) Within the same class, a ring or ring system has seniority over a chain. When a ring and a chain contain the same senior element, the ring is chosen as parent. Rings and chains are chosen regardless of their degree of hydrogenation. As a consequence, this approach prefers the choice of a ring over a chain in systems composed of cyclic and acyclic hydrocarbons.
  
  (2) The context may favor the ring or the chain, so that, for example, substituents may be treated alike or an unsaturated acyclic structure may be recognized, or the one chosen has the greater number of skeletal atoms in the ring or in the principal chain of the acyclic structure.
  
  (…) For selection of a preferred IUPAC name, see P-52.2.8.


 


  P-52.2.8 Selection between a ring and a chain as parent hydride
  
  Within the same heteroatom class and for the same number of characteristic groups cited as the principal characteristic group, a ring is always selected as the parent hydride to construct a preferred IUPAC name. In general nomenclature, a ring or a chain can be the parent hydride (see P-44.1.2.2).


Therefore, the preferred IUPAC name (PIN) of the compound that is given in the question is 1-ethyl-2-hexylcyclopropane.



In general nomenclature, however, the context may favour the chain, so that the parent structure has the greater number of atoms in the principal chain. The corresponding systematic name for the compound given in the question is 1-(2-ethylcyclopropyl)hexane.

Note that according to the obsolete 1979 recommendations, a hydrocarbon containing a small ring attached to a long chain was generally named as a derivative of the acyclic hydrocarbon. Many books are based on these nomenclature rules and thus may expect an answer that favours the chain.