As discussed under 1 Nephi 14:28, the original text allowed for not to precede a but-phrase. The 1920 LDS edition removed the not here in 3 Nephi 6:16, but the critical text will restore it. The motivation for removing the not here is not strong, nor has it been consistently applied elsewhere in the text (for instance, not in Jacob 4:1: “and I cannot write but a little of my words”). For a fuller discussion of multiple negation in the original text, see under negation in volume 3.
Summary: Restore the not here in 3 Nephi 6:16: “they had not enjoyed peace but a few years”; there is evidence elsewhere in the earliest text for this kind of negation.