A Question about a Question related to Graph Theory and Maximum Flow
It's asking you to prove that there exists a sequence of $|E|$ augmenting paths that yields the maximum flow.

The hint suggests: suppose you already knew the maximum flow.  Then use that information to choose $|E|$ augmenting paths, that will yield that maximum flow.

Yes, this sounds weird.  Obviously what you have proven will not be useful as a maximum-flow algorithm (you would need to know the maximum flow already, so it's no use in computing the maximum flow).  Think of it as proving a theoretical fact, rather than trying to design a useful algorithm.