We consider the real Lotka-Volterra cubic system of diferential equations ≡−++++=≡+++++=).,()2(),,()1(021120312221112021221230yxQybxbybxybxbyyyxPyaxayaxyaxaxx&& (1) For (1) the origin of coordinates )0,0( is a )2:1(−resonant singular point. A straight line ,,,,0Cyx∈=++γβαγβα)0,0(),(≠βα is invari-ant for (1) if there exists a polynomial ),(yxK such that the following identity ),()(),(),(yxKyxyxQyxPγβαβα++≡+ holds. We say that an invariant straight line l has algebraic multiplicity equal to m if m is the greatest natural number that ml divide()()yxyxPQPPQQQQPP′+′−′+′. In this paper we give a clasification of systems (1) with six invariant straight lines of two directions. Theorem. The system (1) has invariant straight lines of two directions of total algebraic multiplicity six if and only if it has one of the following eight forms: 1. +−=−−=),2)(1(),1)(1(byyyyaxxxx&& 2. +−=+−−=),2)(1(),1)(1(byyyyaxxxx&& 3. −−=−=,)1(2,)1(22yyyxxx&& 4. +−=−=),2)(1(,)1(2byyyyxxx&& 5. −+−=−−=),23)2((),1)(1(2xxayyaxxxx&& 6. +−−=+=),2)1)((1(),1(2ybyyybyxx&& 7. +−=++=),2)(1(),1(2byyyypxqxxx&& 8. −=−−=),2(),1)(1(2qyyyaxxxx&& where Rpqba∈,,,.