to act amicably in Fortunato's presence and waits until the carnival season to enact his revenge. He tells his servants that he will be leaving town in order to assure that no one will be at his palazzo and runs into Fortunato, who is already intoxicated. Montresor then lies to Fortunato by telling him that he has a cask of rare Amontillado wine, knowing the entire time that Fortunato will not hesitate to try it. After leading the intoxicated Fortunato deep into the catacombs of his palazzo, Montresor ends up shackling his enemy to an alcove and proceeds to build a wall around Fortunato. Montresor murders Fortunato by burying him alive. Fortunato more than likely died of asphyxiation or starvation behind the wall that Montresor erected.

Montresor does not actually directly kill Fortunato.  What I mean by that is that Montresor does not do something like strangling or stabbing or shooting him.  What Montresor actually does may be worse than that.  He gets Fortunato down into his wine cellar and then he chains him to the wall.  When he is chained, he builds a brick wall around him.  Now, Fortunato is down there and can't get out.  He will, presumably, die of lack of water in a few days.

So, you can answer it in a coupleof ways, I guess -- he kills him by walling him up or he kills him by not giving him water.  One of those would be how I'd answer that.

Montresor kills Fortunato, so he gets the revenge he feels he deserves and rids himself of a perceived adversary, but there is no real sense that he resolves his conflict with his enemy. To resolve a conflict would involve, at the least, talking it out, and this never happens.

Although Montresor asserts that Fortunato has injured him a thousand times, during the course of the story, Fortunato appears completely unaware that Montresor has any reason to be angry with him. Montresor himself says he has hidden his anger well, smiling and being friendly to Fortunato so that he can more easily get vengeance.

While he sobers up and recognizes he is being walled up in a catacomb, Fortunato undoubtedly realizes that Montresor is upset with him for some reason, but he seems to have no idea what the problem is. Fortunato has no opportunity to apologize or, conversely, to explain how what happened was a misunderstanding. Montresor simply leaves him to perish.

One could answer the question of Montresor resolving his conflict with Fortunato (from Poe's Story "The Cask of Amontillado") in two very different ways.

First, one could look at the fact that Montresor is able to resolve his conflict with him by ridding himself of the physical problem (Fortunato's life). By ending his life, Montresor has rid himself of the physical reminder that Fortunato still walks alive and well.

Another way one could look at the conflict resolution is that the internal conflict will never be resolved. Sometimes ridding ones self of the physical problem does not rid one of the mental conflict.

What this means is just because Fortunato is dead does not mean that his insult against Montresor will disappear. In fact, one can carry a grudge against the dead as easily as one can carry a grudge against the living.