Imagine that two unlinked autosomal genes with simple dominance code in goats for size, where l is large and l is small, and for color, where b is brown and b is white. if a small, white male goat mates with a large, brown female goat of an unknown genotype, what is the probability that they would produce small, white offspring?

1)
T- tall allele;
t- small allele;
B-brown allele
b- white allele

The male has recessive traits for bothe the height gene and the color.
He is small and white and to express these traits it means his genotype  is: ttbb. 
He has both alleles, of each gene, recessive to express his caracteristics.

2) The female genotype is unknown but we know she is tall and brown.
There are 2 possibilities for her genotype:
TTBB or TtBb
In the first case, she would be dominant homozygotic -both alleles, of each gene, are dominant.
The second case, she would carry a recessive allele and a dominant allele. This makes her heterozigotic for both genes.

3)Due to the two possibilies of the female genotype, there will be two different results for the probability of the offspring.
First : ttbb x TTBB- the probability of having small and white offspring would be 0%. That's because the offspring would be: TtBb- expresses the tall and brown traits.

Second: ttbb x TtBb- the probability of having small and white offspring would be 25%. That's because 1/4 of the offspring could have the genotype ttbb.For better understanding i made the punnet square (see the blue part).

You didn’t give us any choices