Why does the Greek Alphabet have no 6?

The Greek alphabet doesn't have a "6" because the concept of a numeral "6" as we know it didn't exist in the way it does in our modern number system when the Greek alphabet was developed.

The Greeks used a different system for representing numbers, using letters of their alphabet to represent numbers. Different letters represented different numbers. They didn't have a single character dedicated to the abstract concept of "six" separate from the process of counting. They would express the number six using a letter (ς, or stigma, a form of the letter "s", in the case of six). The system wasn't based on positional notation like our base-10 system, and so there's no need for a specific symbol representing a specific place value.