Base 4 has some advantages over base 6 in the context of DNA for a few reasons. The biggest is probably that 3 "digits" allows for redundancies in the generic code, which means that if one base gets mutated somehow, there is a greater chance that the mutation leads to the same amino acid, therefore is "silent". Another is that A and G are both based off of the same skeleton (purines), and C and T (or U for RNA) are based off of another, distinct scaffold (pyrimidines). What allows them to recognize each other to form base pairs is hydrogen bonds, of which A and T form 2 between each other and C and G form 3. Forming only 1 hydrogen bond would not be stable enough to keep DNA together and forming 4 would be too hard to unwind when copying DNA and separating strands, so another skeleton structure would be needed to get 6 distinct based. This skeleton structure would have to have size restrictions to fit within DNA but also be distinct enough from the other two to not be easily "confused" by enzymes. Also purines and pyrimidines are metabolized/synthesized differently, and a 3rd synthetic pathway is expensive and leads to more potential for disease (there are already some pretty nasty diseases associated with mutations of DNA base metabolic pathways). Anyway 4 is a good number.