What did each of Dante's four enemies hope to gain by their actions?
In the novel, The Count of Monte Cristo, there were four things the enemies of Dantes wanted for themselves.
1) Fernand was in love with Dantes' fiance, Mercedes, and wanted her for himself. With Dantes out of the way, Fernand was free to woo her affections and finally won her over to marrying him.
2) Danglars wanted the position of captain of his own merchant ship, but his employer give it to Dantes instead. So, the jealous Danglars accused Dantes of being a traitor hoping he'd be condemned and sent to prison. With Dantes gone, Danglars could then be appointed captain of the ship.
3) Villefort, the royal prosecutor whom Dantes was brought before when accused of treason, destroyed the only evidence there was to prove Dantes' innocence and had him condemned to prison to keep him quiet.
4) Cadderouse, a former friend of Dantes and who could have kept him out of prison had he intervened, was more interested in the money he was paid by the others to put Dantes in prison.
So, to summarize, Fernand wanted Dantes' woman, Danglars wanted his captain's commission, Villefort wanted to protect his political position, and Cadderouse wanted to get rich.
In the end, Dantes took from all four of his enemies the things they'd taken from him.