Molecular electronic state symmetry
Each of the terms you generate has a different energy, and may have different spin multiplicity. The spin multiplicity $(2S+1)$ is given by the left superscript (6 and 4) . The quartet (right) it seems has the lowest energy with spin of a triplet (sym e) x doublet ($b_2) \to$  triplet + quartet.  To do this add spin vectors triplet $S_T=1/2+1/2$ , doublet $S_D= 1/2$ and  make series $S_T+S_D \to |S_T-S_D|$ in unit steps, (Clebsh-Gordon series) this gives total spin 3/2 &amp; 1/2 or quartet($\uparrow\uparrow\uparrow$) + doublet($\uparrow\uparrow\downarrow$). The symmetry has next to be associated with the spin multiplicity and this is complicated. It is necessary to find the character ($\chi$) under, say, quartet multiplicity for each symmetry operation $R$ for each symmetry species $A_1,A_2 ..$  etc. $R^2$  means square the operation. In this case this is 

$$\chi(quartet) = (1/6)\left([\chi(R)]^3-3\chi(R)\chi(R^2) +2\chi(R^3)\right)$$

The result has to be reduced into symmetric $\chi^+$ and antisymmetric components $\chi^-$  as $\chi^+=\left( [\chi(R)]^2+\chi(R^2)\right)/2 $ and   as $\chi^-=\left( [\chi(R)]^2-\chi(R^2)\right)/2 $ and the set of characters produced reduced to find the symmetry species.

Chapter 5 of 'Symmetry &amp; Spectroscopy' by Harris &amp; Bertolucci gives a detailed account of how to do this.