Skin color in a certain species of fish is inherited by a single gene with four different alleles. how many different types of gametes would be possible in this organism?

4

Explanation:

According to Mendel's law of purity of gametes, each gamete contains single allele for a gene. The alleles of a gene segregate during gamete formation and each gamete has one allele for a gene irrespective of the total number of alleles for a gene.  

If the gene for skin color in a fish species has four alleles, an individuals fish would have only two alleles which in turn would segregate during gamete formation.

Since there are four different alleles of the gene (let's assume a,b,c, and d), total possible gametes produced by this organism will be = 4. A gamete can have one of the total 4 alleles making total 4 types of the gametes each with a or b or c or d allele.