It is "an-deachair" to hear the pronunciation of "ag déanamh". This one came up as a "Type what you hear" and I was baffled since I am more used to Munster.
Why isn't it "oibre", since objects of verbal nouns are supposed to be in genitive?
This is an example of a noun that is “nominative in form, genitive in function”. There are several instances in Irish when a genitive noun takes the nominative form. This sentence is representative of one such instance — when a qualified indefinite noun is governed by a verbal noun, the indefinite noun remains in the nominative form.
It’s the same principle, but the contrast would be ag lorg na mná áille (“searching for the beautiful woman”, using the genitive singular forms of bean and álainn) vs. ag lorg bean álainn (“searching for a beautiful woman”, using their nominative forms despite being functionally genitive).
I can hear the amh between déan and aon. But remember that déanamh is only pronounced with a terminal "v" sound in Munster Irish, so it sounds more like "daynuh" from the Duolingo speaker.