Brown (B) is dominant to white (b), and tall (T) is dominant to short (t). What is the probability of producing a brown offspring from two...

By considering the information given and the relationships between phenotype and genotype, we can definitely conclude with the initial information: 

B = brown, dominant

b = white, recessive

Therefore BB and Bb will be brown, and bb will be white.

T = tall, dominant

t = short, recessive

Therefore TT and Tt will be tall, and tt will be short.

We are told that both parents are heterozygous; in this case, we're looking specifically for brown offspring. Because of independent assortment and the fact that the color gene appears to have nothing to do with the height gene, we can simplify this problem; the T and t alleles will be irrelevant. We only need to look at the B and b alleles.

We know both parents are heterozygotes, which means both parents are Bb. 

This means they have a 25% chance of having BB children, 25% for bb, and 50% for Bb. 

Again, the T and t alleles are irrelevant here because the color of the children is a totally separate ratio from the height.

Since we're only looking for brown offspring, and 75% of the children will have a dominant B allele, then 75% of the offspring will be brown.