The most common and most likely answer to this crossword clue is the 4 plus 4 plus 4 letter word SALT LAKE CITY
I've seen this crossword clue in The Guardian
S
A
L
T
L
A
K
E
C
I
T
Y
Buddy explains!
The straight part
We know that "American capital" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case american capital = salt lake city.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.