A complete pedigree of six generations, counting yourself as the first generation, would have a total of 62 people including your parents and not counting you. If you count your parents as the first generation the total number of people would be 126 but normally, you are counted as the first generation in genealogical methodology. See FamilySearch Research Wiki, Genealogy Numbering Systems (National Institute). Now, the number of additional people, including the descendants of all those grandparents, can be in the thousands. Here is a chart from the FamilySearch Research Wiki articles I just cited.
How far back in time would you go to research all of your 3rd great-grandparents (the sixth generation)? The answer to that question also depends on how long each generation lived and when they had their first child and if you are descended from the first or last child in the family. Also, whether or not you end up with 62 people depends on available records and whether or not the mother or father of a direct line ancestor is known at all in any record. Many genealogists think they have completed their genealogy when they get back a few generations of one or two lines, usually their paternal and maternal surname lines. When you realize that the sixth-generation number means that you have far more surnames, in fact, 32 to be exact unless someone managed to marry a cousin.
I can give an example of the birthdates of my sixth generation ancestors. The most recent date is 1829. The most remote date is 1761. To go back one more generation and identify their 124 parents you would have to research back into the early 1700s on every line. By the way, because the numbers, at least, double every generation, automatically have an exponential increase in the amount of research and an equal increase in the difficulty of finding and researching the records.
It is quite common when people find out I do a lot of genealogy, to ask me “how far back to you have your genealogy?” I usually give a vague answer because if all I had done for the last forty years was to work on one ancestral line and assuming that the line did not end or records run out, I could be back quite some time. But in the real world of my own genealogy, some of my ancestral lines end in the seventh generation simply because there are no more records. Genealogy is not a game to see who can go back the furthest or accumulate the most names.
If you work back systematically and not only document all of your ancestors but also all of their descendants, you will have plenty of work to do in the first six generations. Fortunately, we can pick and choose which family lines we want to focus on.
Let’s suppose that your goal is to find a royal line or “prove” that your ancestor was a famous person. Then you probably don’t care about all the other names or family lines and you will be missing almost everything there is about genealogical research that makes it interesting and challenging. Finding out that your ancestors were poor tenant farmers or coal miners may not be as impressive to some as finding a royal ancestor, but it is a lot more of a challenge when you do find someone as difficult to find as the common people beginning in the mid to early 1700s. Since none of sixth-generation ancestors left a lot of money to their children or grandchildren, I have learned to find out about them and their lives and that is wealth enough for me.
If you have a well-documented genealogy going back six generations on every line, you have really accomplished something very few people can or would want to do.