How can I analyze Hemingway's story "Hills Like White Elephants" using Freud's theories from Letter 52 to answer, referring to the unconscious...

This complex question can get only the briefest answer in
this format but it will guide you to further thought and investigation. Freud's letter
to Wilhelm Fliess, dated Vienna, November 14, 1897, discusses the the
concept of what later came to be translated as
"afterwardness," a vague and obscure label for a concept that relates to
Freud's attempt to definitively identify the mechanism of
"repression."

In the original letter
written in German, Freud uses the word "Nachträglichkeit," later translated as either
"afterwardness" or as "deferred action," to define the concepts
discussed.

A
release of sexuality ... comes about ... from memory traces -- therefore also by the
path of deferred action. ... [in which] the preconscious and a sense of consciousness
turn away from the memory.  This is repression. (Nov 14,
1897)

Freud's simply stated
idea in this letter has been enlarged upon by Freud and others to suggest in essence
that an action or event in a person's early years can lie dormant until later more
mature years when that memory might be revived or suggested by later circumstances and
that the generation of that memory might trigger a rejection--a deferred action of
rejection--from the person concerned.

The way this might
apply in analysis to the American man and to Jig, who
omit the overt mention of the topic of Jig's debated
abortion, is that Jig is having a deferred action of
rejection against the memory of her intimacy with the American man since
he is using that intimacy to compel her to undergo an abortion, an idea that is
apparently abhorrent to her. If the idea of "repression" is
taken out of context of "afterwardness" as discussed in Freud's letter, it might be said
that Jig is willing to "repress" her feelings of repulsion to abortion in order to
placate the American man.

It seems though, that these
analyses might be misapplying the concepts as Freud discussed them in his letter to
Fliess since Freud makes it clear in the letter that his idea applies to two stages of
life: the early physiologically immature years where an incident occurs and the later
physiologically mature years when the deferred reaction/rejection/repression of the
early memory occurs.