So I know that Hemoglobin is made of 2 alpha and 2 beta subunits. The alpha consists of 2 genes on chromosome 16, and the beta of 1 gene on chromosome 11. So why does Hemoglobin only have 4 alleles? Why is it not 6? In my way of thinking each alpha subunit consists of 2 genes, so 4 total. And each beta subunit consists of 1 gene, so 2 total. Together that makes 6. Confused! Thanks in advance
Meaning of Allele
The word "allele" is often used with two slightly different meanings in biology.
The first, probably more appropriate usage is the one in Remi.b's answer: an allele is a variant of a gene in a population; there are many many possible alleles for a given gene, depending on the length of the gene, though typically only a few are common in a population and even fewer may be known.
The second use of the word "allele" is to mean "copy" of a gene; because those copies can be different, in this context an allele is a potential variant of a gene in an individual. For a diploid organism like a human, you might say that an individual has "two alleles" but what you really mean to say is that individual has "two copies of a gene, which could be the same or different alleles." The relationship between the two copies is called zygosity. I'd argue that this is a slightly sloppy use of the term, but nonetheless it is common and if you understand the meaning it is still clear.
Genes for hemoglobin
For hemoglobin, there are at least 3 important genes: two each encode alpha subunits, and the third encodes the beta subunit (there is also a delta and gamma subunit, but we can omit discussion of those for now).
For the beta subunit, each individual has two copies of the gene, which in human populations are typically thought of as one of two population alleles: either a normal allele or an allele associated with sickle cell anemia. Individuals with two of the sickle cell alleles will have sickle cell anemia.
For the alpha subunit, each individual has two copies of two different genes. There are alleles for each of those genes that produce non-functional products. Individuals with alleles that produce non-functional alpha subunits, for either gene, have Alpha-thalassemia. The severity of Alpha-thalassemia depends on how many alleles are present across the two genes that do not product functional alpha subunits.
Why 4 alleles for hemoglobin??
I suspect if you read somewhere that there are "4 alleles" for hemoglobin, that source was probably talking about Alpha-thalassemia in particular, in which case there are indeed 2 copies of 2 different genes so that an individual has four possible alleles. The severity of Alpha-thalassemia depends on the total number of defective alleles across the two genes, where having 4 defective copies is fatal, and having just 1 defective copy is not noticed clinically.
In the population, however, it is likely that there are actually many other alleles for each gene. For the purpose of describing disease, however, we can group these into "functional" and "non-functional" and say that there are two population alleles for each of these two genes.
An allele is a variant at a given locus. If at a given locus, there is no variance in the population, then the entire population is fixed for a single allele. If there are different variants in the population, then there are severeal alleles in this population.
A locus can be defined as a DNA sequence of any length. For a locus of size
n the maximum number of alleles is $n^4$ and the minimum number of alleles is $1$. In practice, that being said, we sometimes group allele together and hence the maximal number of alleles is somewhat lower. But let's not go into these details.
The point is that it does not matter how many subunits you want to consider. The number of alleles is simply the number of variants that exist in the population. If for the hemoglobin, there are 6 alleles, then there are 6 alleles!