Suppose Maria wants to breed parakeets that are yellow with patterned feathers. However, when she bred several parakeets that were yellow with patterned feathers, she found that there were four different offspring phenotypes. Phenotype Number
patterned yellow wings 18
solid yellow wings 6
patterned white wings 6
solid white wings 2

Number of genes and alleles?
2 genes; 2 alleles each
1 gene; 4 alleles
4 genes; 1 allele each

Which phenotypes are coded for by the same gene? Different genes are separated by semicolons?
yellow and white; patterned feathers and solid
yellow and patterned feathers; white and solid
all by the same gene
each by a separate gene

Explanation:

First let's define a few things.

An allele is a variant form of a gene, each gene can have two or more possible alleles, one inherited from each parent. The copies, however, are not necessarily the same. When the copies of a gene differ from each other, they are known as alleles. A given gene may have multiple different alleles, though only two alleles are present at the gene’s locus in any individual. Alleles can sometimes result in different phenotypes (observable traits), with certain alleles being dominant. (overriding the traits of other alleles)

Let's make a table of our bird's alleles.

We can see from the phenotype of her bird's offspring, yellow is dominant over white, and patterned is dominant over solid.

Let's use Y for dominant yellow, w for recessive white, P for dominant pattern, and s for recessive solid. I know dominant and recessive traits usualy use the same letter with recessive traits being lower case, but in this case it makes it easier to determine phenotype.

Our parent birds are dihybrid cross which involves 2 genes coding two traits, with dominant yellow pattern both represented by PPssYYww.

So look at the chart. It has then been color coded by the traits the bird will exhibit. We have:

9 birds with Patterned Yellow Wings

3 birds with Solid Yellow Wings

3 birds with Patterned White Wings

1 bird with Solid White Wings

This is the same ratio Maria found in the phenotypes of her birds.

Now we can answer the questions:

Number of genes and alleles? We can see that there are 2 genes, one gene for pattern, and one gene for color, but there are also 2 alleles the variant of the Pattern and the variant of the color.

Which phenotypes are coded for by the same gene?  

yellow and white; patterned feathers and solid - This one as you can see from the phenotype chart, and as discussed earlier, there are 2 genes, one for color, the other for pattern.

yellow and patterned feathers; white and solid

all by the same gene

each by a separate gene