I am playing with my friends a combined version of Vampire. In that world there are some werewolves, ghosts, and other creatures. I have a mission to make some people stop believing in ghosts and make them believe in the power of blood. I was thinking about summoning one ghost and killing him. Is it possible by the book?
I'm not very familiar with the mechanics of Wraith: The Oblivion, but this forum post shares this information:
Page 58 of The Sea of Shadows:
"If all or most of the damage was normal (i.e., not aggravated), the above holds true. If a wraith loses all her corpus due to aggravated damage, there is no Harrowing; the wraith is dead forever. Aggravated damage is caused by a power of Moliate, when the wraith is Embodied, or by Stygian of darksteel weapons."
So if "Deathlords and high-ranking Hierarchy officials" appear in the physical world using Embody, you can throw any aggravated damage at them and it would work. But if you're targeting a run-of-the-mill average ghost, it's unlikely that they'll be able to cross over.
Or you could get your hands on a stygian steel weapon that was created in the Underworld and somehow brought over into the Skinlands. This is something that I'm guessing would take an absolutely extraordinary backstory to justify or a storyteller ruling that a necromancer using the power Ex Nihilo is allowed to enter the Underworld, grab an object, and bring it back with them. The rules for Ex Nihilo don't mention whether or not this is possible.
You could instead cast the level five Thaumaturgy ritual Warding Circle Versus Spirits / Ghosts, which would create the effect of banishing any spirits in a particular area, like a haunted house. With some subterfuge, that could be presented as a character "killing" those ghosts.
You could also use the Necromancy power Compel Soul and, on an exceptionally high roll, force a ghost to do something that puts it "in immediate peril of destruction", like stay inside of a Warding Circle.
The wording of the Necromancy power "Haunting" says that
A wraith attempting to leave the area of a haunting must make an extended Willpower roll (difficulty 9, four cumulative successes necessary in a single scene) or take a level of aggravated damage for each roll. If the wraith runs out of health levels, it is hurled deep into the Underworld to face destruction.
so you could theoretically both bind a wraith in place with Haunting and then use Compel Soul to force it to try to leave the area of effect and be destroyed in the process.
The Necromancy power Torment allows a vampire to inflict lethal damage on a ghost (who is perhaps held in place with Compel Soul or Haunting), which can have the appearance of killing the ghost, but only banishes them for a month. Still, that would probably get the reaction that you wanted.
I'm sure there are plenty of other options in the World of Darkness, but that's all I could dig up from a quick glance through the V20 rulebook.