Oh, this is problematic. As far as I am aware, it is supposed that /kʷ/ is a phoneme – a labialised velar plosive. If this is true then /kʷot/ would likely actually have been pronounced as 'kot' (not in an American accent! Think an English accent) because there is no glide, [k] stays where it is.
I've just checked, if this can be correct by looking at words derived from words with the cluster quo. For example French coter from quot-are. No glide there. Also, none of the words derived from Latin quod have a glide. This is evidence that /kʷot/ wasn't [kwot] in Classical Latin
The main question is if the same sound wasn't an allophone of /k/ in front of /o/ and if even more labialisation could have been enough to maintain this distinction. Were there even minimal pairs?
Be careful with French, there is the ancient French pronunciation, that is very different from the Modern French. You need to be sure the sound sounded "k" in Ancient French, not Modern French. Ancient French tends to pronounce more letters than Modern French. (as we can often see it in the English word borrowed)
For instance, "quatre" in Modern French is "katr", and in Old French, it was pronounced "kwatr"
IPA(key): (early) /ˈkwatrə/, (late) /ˈkatrə/
Quoter did exist in Old French, but not in Modern French.
It's probable that Quoter stopped to sounds like with a "w" and the spelling has been simplified in "coter"?
Like many sentences in Duolingo, if you imagine a specific context, it can sound a little more natural.
Recalling that Rome was in the region named "Latium", imagine that you have school-age children and are thinking of moving to Rome from some distant province. I tell you "there are twenty schools in Latium". You might ask either
"How many of them are in Rome?" or
"How many schools are in Rome?" (slightly stressing the word "Rome")
One czech author has written a latin book called: "schola ludus" which is translated into czech as "School as(by/with) a game". How is it possible that "ludus" means here schools? And is it than possible to translate school as a game as Ludi ludus? (It reminds me a russian sentence: Peace to the world = Mir miru.)