Ican t imagine any reason he should have behaved in such an extraordinary way. for

I can't imagine any reason "why" he should have behaved in such an extraordinary way. If we were to use "how" in that sentence it would contradict the context. We are obviously talking about a situation that has happened so we know that "he" has in fact acted in an extraordinary way but we don't know "why" he acted that way. Therefore "why" is the correct term to use.

The answer is incremental backup as this is the one responsible of having to provide a backup with files that are modified since the last backup it has received, it is considered to be a backup in which is a type of security copy.