word-forming element used freely in English, "between, among, during," from Latin inter (prep., adv.) "among, between, betwixt, in the midst of" (also used extensively as a prefix), from PIE *enter "between, among" (source also of Sanskrit antar, Old Persian antar "among, between," Greek entera (plural) "intestines," Old Irish eter, Old Welsh ithr "among, between," Gothic undar, Old English under "under"), a comparative of root *en "in."
A living prefix in English from 15c. and used with Germanic as well as Latinate words. Spelled entre- in French; most words borrowed into English in that form were re-spelled 16c. to conform with Latin except entertain, enterprise. In Latin, spelling shifted to intel- before -l-, hence intelligence, etc.
"to twist strands together to form twine," c. 1300, from twine (n.) and probably also from Old Norse tvinna "to double." Sense of "to twist around something" (as twine does) is recorded from late 14c. Related: Twined; twining.
<a href="https://www.etymonline.com/word/intertwine">Etymology of intertwine by etymonline</a>
Harper, D. (n.d.). Etymology of intertwine. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/intertwine