[A brief description that will lead you toward a deeper analysis is all that the eNotes format can provide. You will be able to develop all the detail you need afterward.]
First let's clarify definitions. A plot line is the story line: who did what when to whom, where, why, how and with what. The story line is different from the structure. The structure is how a plot line is shaped. It includes questions about exposition, rising action, climax, etc, in terms of how a specific story may or may not fit the general theoretical model of universal narrative structure. So what you are really asking is what is the story structure as understood according to the six divisions of structure.
Having said that, the exposition, or introduction, presents the central characters, the setting, the mood and the problem, or conflict, of the story. In this case, it begins with Poirot at the train platform in Aleppo, having just successfully finished a case for the French Army ("You have saved the honour of the French Army"). He is about to board the Taurus Express to return to Europe after first taking a few days stay in Constantinople. It ends with the inciting moment when Poirot receives a telegram while in Constantinople and takes passage on the Orient Express instead.
The rising action comprises those events that complicate the conflict and escalate it. The conflict in this particular story is introduced when Ratchett approaches Poirot asking for his protection against a murder attempt. Poirot declines because of Ratchett is "more malevolent than benevolent." The rising actions follow and include the investigatory interviews and deductions Poirot conducts and makes following the nighttime murder of Ratchett.
The climax is the moment when the decisive action or decision is taken by the principal character, the protagonist, that determines the ultimate outcome of the story. Some make the mistake of thinking the climax is always the most emotional or most action-packed moment, but it may also be a quiet moment when a cognitive process is completed or when the decisive decision is made. In this story, the climax comes after Poirot has tested his hypothesis and the stories of the twelve unravel and Poirot announces the culprits.
The falling actions are those events that occur after Poirot solves the mystery. The resolution, or denouement, occurs when he, M. Bouc, and Dr. Constantine choose to withhold elements of the investigation and conclusion from the police and claim Ratchett's death was the work of a single assassin who escaped detection and apprehension.
"Without knowing it, he lost a button of his uniform, Then he slipped out of the compartment and along the corridor ... a few minutes later, dressed in ordinary clothes, he left the train ...."