Note/Warning! It is very possible to contract the virus that leads to Vampirism during this quest. Just an FYI. If that's what you want, good, let the vampires keep hurting you until you get it. If not, you can use a "Cure Disease" potion to snub it out in it's infancy IF you get it.
Now if you're decently powerful, this job isn't nearly as hard as Nazir made it out to be. Sure, they're vampires, but not immortal. Hern and Hert both live in the Half-Moon Mill (although Hert won't always be present; making it even easier). The best part is there will be no other witnesses .
That last part is important, because you can stroll into the house when they are both there, proceed to attack them (and rack up a big fine in the process) and then kill them. When you kill them, the fines and bounties on your head will go away since you killed the only witnesses.
Loot the place if you wish, then report back to Nazir. On your way to see him, Astrid will greet you and talk about what happened between you and the Night Mother. She agrees that you must go do as the Night Mother said, and will thus trigger the next quest in the chain: " The Silence has been Broken ".
Be sure to see Nazir about your reward for this quest though (and the previous one, if you haven't collected yet). This contract is worth 500 Gold .