Wiktionary lists it, having a reference to Lovecraft having used it at least once as a synonym of technique. It seems to be a very rare word in English.
The thing is that "technique" and "technology", map to "техника" and "технология", but the mapping is not perfect, as техника has multiple meanings and some of those meanings are captured in the English word "technology" (but not others, which are indeed captured by technique or the very rare word technics).
So I think that using "technology" or just "tech" is better and more natural in English here, but since we are learning Russian, one must be careful to understand that in Russian these two words do not work the same way.
Of course, single sentences without context as in Duolingo have many translations. "I like the technique" seems like a valid translation of the isolated sentence (maybe, say, a dance or piano teacher judging a student performance?), although it does not quite match the theme of the rest of the lecture, which suggest "tech" is intended.
So what's really going on is we're arguing over a word that is not proper English. No wonder we don't know what technics should translate to. I bet no one knows what "|dotonno" translates to either. That is because it is gibberish. "Technics is a brand name of the Panasonic Corporation, a company that produces a variety of electronic products." It was made up by Panasonic.
"мне нравится текника" yeah, it's wrong...... how can one use Duo learn to spell correctly if Duo doesn't draw attention to "typos". You threw that little help away. It is ON SOME (I think the older stuff) but not on others. It makes Duo less attractive. Dont bother down arrowing, I ususlly remove my dummy spits after a week or three