How many different combinations of these alleles would be possible?

If crossing over occurs between these genes, then the inner two chromatids would be affected by the crossing over and the outer two chromatids would be of the parental type.

From the blue eyes/brown hair chromosome these two combinations are possible, assuming the part with the hair color gene was recombined:  
  blue eyes/brown hair
  blue eyes/blonde hair

From the green eyes/blonde hair chromosome:
  green eyes/blonde hair
  green eyes/brown hair

So the answer is four different combinations of alleles (two parent-type chromatids and two recombined chromatids).

4 combo's-
blue eyes brown hair
green eyes brown hair
blue eyes blonde hair and
green eyes blonde hair

although i think the 2nd and 3rd ones would open happen if crossing over happened (recombination)