I’m not the best person to explain it (I only mock it), but the way I understand it, the 6,000+ number comes from a literal reading of the Bible, and using its stories of generations of Jews from Adam on to calculate the passage of time from Creation to Christ’s age.
the passage of time from Creation Of Adam to Christ’s age.
One can argue "the time from the creation of the sun, until Christ's age" but the "days" of creation before that cannot be determined as to their length, because the sun did not yet exist so neither could the concept of a 24 hr day.
Also it should be noted that the bible uses different wording in reference to those first "days"