Q: I have heard that there are references to the Torah containing 600,000 letters. However, we know that the Torah actually has a bit more than 300,000 letters.
Do you know of an accurate system of correlating this to come up with the 600,000 number?
A: Your question is very well known. There are several answers.
A very logical explanation appears in Likutei Torah. There it is explained that the letters include the "characters" of the letters, which are the vowels and the cantillation signs, which are not part of the text. In general, every word possesses twice as many characters when the vowels and cantillation signs are included. That brings the total number to 600,000 as opposed to the almost 300,000.
Sometimes the letters are divided into components, such as an Alef being one Vav and two Yuds. This explanation does not appear in Likutei Torah.
Every letter has its full name. There are different systems for filling in the letters — either with two other letters, or one other letter. If it is filled in with just one other letter, that also brings the total from 300,000 to 600,000. This explanation also does not appear in Likutei Torah.