Explanation:

To predict the offspring's hair color using a Punnett square for codominance, we'll use the symbols B for blonde and G for grayish hair.

The father is homozygous white (BB), and the mother is homozygous black (GG). In codominance, both alleles are expressed, so their offspring will have one allele from each parent.

Let's create a Punnett square to see the possible combinations:

B G

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B | BB BG

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G | BG GG

Based on this Punnett square, the possible offspring genotypes are BB (blonde), BG (a mix of blonde and grayish), and GG (grayish). So, the offspring's hair color would include a mix of blonde and grayish due to codominance.