2 Peter 2:5 (Mounce Reverse Interlinear New Testament) :
and if he did not spare the ancient world (but preserved Noah, the eighth, a herald of righteousness) when he brought the deluge on an ungodly world;
The phrase in bold is from the Greek ogdoon/ogdoos
Strong's Concordance assigns this word #3590:
- definition: "the eighth"
- usage: the eighth, one of eight, with seven others
Referring to dozens of English translations, the oldest and newer, and a few intended for converts from Judaism, reveals that almost every usage is of the "one of eight" or "with seven others" variety, and usually with the added (but not indicated) word "people". This makes the term a simple reference to the whole family that entered the Ark (four men and their wives).
A few versions, mainly archaic or pure literal translations, leave it as "the eighth" with no clarification.
The Englishman's Concordance gives examples of this word followed with "person" or "day".
A few explanations can be found online that attempt make this term a reference to the idea of Noah being a sort of re-beginning, since the Old Testament has descriptions of various events that last seven days, so the eighth day would be a new start. Or possibly an event occurs after seven months of something, so it may be considered the eighth.
Or could this be a reference of some kind to the idea that there were seven pairs of each clean animal admitted to the Ark, so humanity is the eighth? Or that they all waited in the Ark for seven days so this re-beginning began with flooding on the eighth?
The entire chapter is about how God destroyed all the people except Noah and his family, then mentions saving Lot from Sodom but doesn't mention his family (Lot was not called "the fourth"). If making the argument this is because Lot's family wasn't righteous, they were just along with Lot, then include in your reasoning why Noah's family was as righteous as Noah.
If making the argument that Noah was the eighth person in a line (type or genealogy), thoroughly explain your reasoning why the first person in that line is significant.