For Sequence Probabilities topic, how to obtain the last 2 expressions in the screenshot below ?

Sorry about replying this late to it, if you’re still having this problem, or if anyone else is having this problem, I’m adding a reply.

So the markov assumption here specifically is that the next element in a sequence solely depends on the current element (or more generally a limited history of the sequence). So the probability P(D|A,B,C) is about the same as the probability P(D|C). The rest is explained in the lecture video so I’d suggest going through it thoroughly.