Usage of lowest locant rule How should we name this compound by IUPAC system? 
Is it 

2,3-dimethylcyclohexene
 (or) 
 1,6-dimethylcyclohexene?

In the first case locant position adds to 2+3 = 5, while in second it is 1+6 = 7. However, in second case, first substituent gets lower position, i.e., 1 , while in first case it gets 2.
According to latest IUPAC recommendations, lowest locant rule is the valid rule followed for organic nomenclature and presently, the lowest sum rule is no longer followed.

So, as you have discussed in the question, the name that follows the lowest locant rule is the proper name of the compound.

So, it is 1,6-dimethylcyclohexene.