The climax is the turning point in a story or a movie. The narrator kills the old man by suffocation. The old man had screamed loudly but the narrator didn't seem to care. "With a loud yell, I threw open the lantern and leaped into the room. He screamed once-once only. I dragged him to the floor and pulled the heavy bed over him."
The falling action is the loose ends in the story being tied. The falling action was the narrator cutting up the old man and placing him beneath the floorboards along with the police coming. The police had come because the neighbors had reported a scream but the narrator said he had a bad dream which caused him to scream. "The police men came in. A neighbor had heard a scream and had gone to the police station. These men had been sent to search the place."
The resolution is how the story wraps up. The resolution in this story is when the narrator admits the he killed the old man right in front of the police. The narrator beforehand had 'heard' the old mans heart beat. He had said "Enough! I admit the deed! Tear up the planks! Here, here! It is the beating of his hideous heart!"