Request How many generations could 4 females and 8 males of an eternally young species produce without inbreeding problem?

For context, I am a writer, and in my story, the main characters are the species who remain eternally young and fertile for centuries. Otherwise they grow up at the same rate Humans do, and the females of this species are only able to get pregnant a few weeks out of the year, the rest of the time, the reproductive parts of their reproductive organs are turned off. This is to solve the problem of females running out of eggs by age 60 or 70 when they can live to roughly 700 without technology.

And when a fight is about to happen, the leader says something along the lines of "If that device is destroyed (gene editing machine) then we'll only be able to birth INSERT NUMBER generations without inbreeding!"

So, important stuff. 12 individuals, 4 females, 8 males, they are the last of their kind and cannot reproduce with anyone else and none of them are related to each other. They have eternal youth and menopause/age isn't a factor, how many generations would they be able to produce without inbreeding, or would they be able to beat the inbreeding problem entirely?

https://redd.it/1q1flnb
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