Well, to me, "six conditionals" refers to mixed conditionals. Click here: http://www.englishpage.com/conditional/mixedconditional.html for an explanation on their function and distribution.
Mixed conditionals are a combination of the three basic, or traditional types:
present simple -> will
1st conditional, or future conditional
EX: If I have the money, I will take a vacation.
past simple -> would
2nd conditional, or present conditional
EX: If I had the money, I would take a vacation.
past perfect -> would have
3rd conditional, or past conditional
EX: If I had had the money, I would have taken a vacation.
Added to that are two more types:
present simple à present simple / present continuous
EX: If I go, he goes, too. source
present simple à present modal
EX: If he goes, she can come, too.
The latter two are frequently used, more so, and not in place of, the 1st and 2nd traditional types, according to one source: http://writing.colostate.edu/assignments/archives/e515/Conditionals1.htm.