To solve this genetics problem, we can use Punnett squares to predict the possible offspring genotypes and phenotypes.
First, let's label the alleles for eye color and hair color:
- Brown eyes: B (dominant)
- Blue eyes: b (recessive)
- Brown hair: H (dominant)
- Blond hair: h (recessive)
The homozygous dominant brown-eyed blond-haired man has the genotype BBhh, which means he has two copies of the dominant allele for brown eyes (B) and two copies of the recessive allele for blond hair (h).
The blue-eyed and heterozygous brown-haired woman has the genotype bbHh, which means she has two copies of the recessive allele for blue eyes (b) and one dominant and one recessive allele for brown hair (Hh).
We can now create a Punnett square to cross these two individuals and determine the possible genotypes and phenotypes of their offspring:
```
| B B h h
---|-----------------
b | Bb Bb hb hb
b | Bb Bb hb hb
```
From this Punnett square, we can see that all of the possible offspring will have brown eyes, since the dominant allele for brown eyes (B) is the only allele present in both parents.
For hair color, the possible genotypes are:
- BB: homozygous dominant for brown hair
- Bb: heterozygous for brown hair
- hb: heterozygous for blond hair
The possible phenotypes are:
- Brown hair: BB, Bb, hb
- Blond hair: none (since the man is homozygous recessive for blond hair)
Therefore, all of the possible offspring will have brown eyes, and some will have brown hair and some will have heterozygous brown hair. None of the offspring will have blond hair, since the man is homozygous recessive for that trait.