The root and words for “six” remained very similar throughout Tolkien’s life. The earliest form of this root was ᴱ√ENE “six” from the Qenya Lexicon of the 1910s, with the derivative ᴱQ. ende “six” (QL/35). In the Early Qenya Grammar of the 1920s, the Qenya word for “six” became ᴱQ. enqe [enkwe] with variant enekse (PE14/49, 82), implying a primitive base ✱enek-. This primitive form was made explicit in The Etymologies of the 1930s, where the root was given as ᴹ√ENEK “six” with derivatives ᴹQ. enqe and N. eneg (Ety/ÉNEK). The root and its derivatives retained this form thereafter.
Tolkien spent a fair amount of time analyzing the origin of this root and the basis for the Q. addition of w in various notes on Elvish numbering systems written in 1968 (VT41, VT42, VT47, VT48). One connection Tolkien regularly made was between √ENEK “six” and √ENED “middle”, as “six” was the “middle” of the duodecimal system of numbering (VT41/16; VT48/9); in this respect it was probably an elaboration of the root √NEK “divide, separate, part” by analogy with √ENED (VT47/16; VT48/9). The Quenya -we may have been either a dual suffix based on “six” as twice three (VT48/10) or it might have been by analogy with other important duodecimal numbers like Q. minquë “eleven” and Q. yunquë “twelve” (48/7). Personally I find the second theory more compelling.
A root appearing in notes on words and phrases from The Lord of the Rings from the late 1950s or early 1960s, serving mainly as the basis for S. naith “angle” (PE17/55). It was also mentioned in a discussion of the death of Isildur at the Gladden Fields, again as the basis for S. naith among other words, where the root √NEK was glossed “narrow” (UT/281-2, note #16). In The Etymologies of the 1930s, N. naith was derived from ᴹ√SNAS or ᴹ√SNAT, but the precise derivation was unclear, and in any cases seems to have been replaced by Tolkien with a more straightforward derivation from √NEK.
The root √NEK also appeared in Quenya Notes (QN) from 1957 with the gloss “deprive”, serving among other things as the basis for S. neithan “one deprived” (PE17/167), which was the name adopted by Túrin after he became an outlaw (S/200). The root appeared again in notes on Elvish numbers from the late 1960s glossed as either “divide, part, separate” (VT47/16) or “divide, separate” (VT48/9), where it served as the basis for √ENEK “six” as the dividing point between the lower and upper set of numbers in the Elvish duodecimal system.
It is not clear whether Tolkien intended all these various meanings for the root √NEK to be connected. For purposes of analysis, I’ve split √NEK “narrow” from √NEK “separate; deprive”, but conceivably the sense “narrow” could be a semantic extension of “separate” or vice-versa.