There are basically two cases. Letting N represent not red, we can either have:
RNRNRN or NRNRNR
Therefore, we need to figure out the ways of arranging 2 blue and 1 white into 3 "N" slots. There are three possibilities for this, corresponding to each of the positions we can place the white. Therefore, since there are 2 cases, we have 2*3 = 6 possible combinations that meet the criteria.
If you have additional questions on combinatorics, please feel free to let me know.