Hemingway's "Hills Like White Elephants" ends ambiguously with the young couple's train arriving and with little indication of what decision about Jig's pregnancy will be made. Nevertheless, there are some inferences that the reader can make based upon the dialogue between the man and Jig.
Interestingly, since Hemingway does not give the male partner a name, this action seems to dispose the reader to regarding Jig's feelings more sympathetically. In addition, since the man does not have to be the one to undergo the "simple" operation, it is easy for him to suggest the abortion and feel that everything can be the same if Jig will go through with it. His remark near the end of the story as he observes people in the bar, "They were all waiting reasonably for the train," implies that to him Jig is unreasonable about the simple solution of their problem of "the only thing that bothers" them. Clearly, then, the man's perspective is selfish throughout the dialogue. So, the only solution to his relationship with Jig is for him to have her full attention and love; a baby will interfere with their carefree life.
However, it appears fairly evident that Jig is not really in favor of having an abortion. She asks the man dubiously, "And you think then we'll be all right and be happy...and things will be like they were and you'll love me?" And, as their converstion about the abortion continues, Jig becomes more and more upset until she finally asks the man seven times, the number representing completion,
"Would you please please please plese please please please stop talking?"
Key to understanding the difference between their perspectives is the Jig's statement "We could have everything" and his reply, "We can have everything." While she means that they will be able to still have their love for each other as well as their love for a baby, the man's statement implies otherwise. For, he means that without a child they can maintain their carefree life of travel, dining and drinking, etc. By his use of the present tense of can, he implies that they must not change their way of life. On the other hand, Jig's use of the conditional tense, could, carries their life to a possible next stage.
Therefore, there seems no solution to their dilemma. Like the symbolic setting that is divided by "two lines of rail," one fertile ground with fields of grain and trees, the other with white hills and land that is brown and dry, Jig and the man are divided in their ideas. Thus, the "shadow of a cloud" that moves across the field of grain seems to foreshadow the disintegration of their relationship.
Assuming that you mean what solution could the characters come to to solve their conflict in the story, possible solutions might be different depending on the point of view of the two characters involved. From Jig's perspective, her conflict with the American might be solved by either conforming to his desire to abort their child or to follow her heart and realize that the American is not the man whom she thought he was and that she needs to live her life with her child and without the American. However, from the American's perspective, the conflict might be solved by having Jig abort the child and revert to her frame of mind before the existence of the unborn child. The story suggests that the solution is that Jig leaves the American--she does not seem to want to follow his will and he does not want what he sees as the burden of a family.
The proper solution for the problem would be for the two people to get married and have the baby. Evidently they are not married at the time of the story. The man is selfish and afraid of giving up his freedom and taking on the responsibility of supporting a wife and child. This sort of selfishness is not at all uncommon among males. There is a similar situation in Theodore Dreiser's great novel AN AMERICAN TRAGEDY which the hero tries to resolve by committing a murder. There is another similar situation in William Faulkner's THE WILD PALMS.