"Det" is pronounced like de(ad)
The voice's pitch and pressure is all over the place here though.
I can't even hear the "d", it sounds like "uh" to me. :( Is my ear that bad, or is it the recording?
I can hear the 'd' on the recording, actually more clearly than many people pronounce it. It can be omitted completely: "di liker'eh"
It's always difficult to hear sounds you're not used to paying any mind though, I had the same problem with French initially. I'd recommend supplementing the course with some outside listening practice as well. :)
To me the second 'd' here sounds like a tap [ɾ], as in American English 'd','t' (and most other languages' 'r').
I was thinking the same thing. It sounds a bit like "De likere." It's like the D is either omitted when following a word that ends in R or the final R sound is pronounced something more like an "American R." I don't remember the IPA character for the latter.