"He does not know it either."
Translation:Det vet inte han heller.
Ah, sorry, I missed that. I'm too tired at the moment, shouldn't have answered in the first place. So if you put him first, in
Han vet inte det heller you get the situation where 'He does not know fact X, and he does not know det either'
Han vet inte heller det, you get 'Person X does not know it, and 'he' does not know it either'
So why put han first?
The main reason to rearrange word order is usually what information structure we want. Generally, we prefer to go from what is known to what is not known, this is called the information principle. Very roughly, sentences tend to put known things in the beginning, and new things in the end.
Now, in this case, han is a pronoun, so we can assume the listener knows who 'he' is. But det is also a pronoun, and we can assume that the listener knows what 'it' refers to, too.
So I'd say Han vet inte det heller and Det vet han inte heller are very close, it's just a matter of how you want to stress or present things.
Between Det vet inte han heller and Han vet inte det heller, there is both the difference of presentation and the other difference I mentioned.
That's actually pretty easy – it's just that the verb has to go in second place in the sentence. So if you put det first, the verb vet goes after it, and if you put han first, the verb also goes right after that. Basically vet just stays put in second place whatever you change in the rest of the sentence.