"From America" translates to из Америки and I know that из will take the genitive case. Америка is a feminine noun (because it ends in а and is a place).
To form the genitive case of a singular feminine noun, you replace а with ы. Америка would become Америкы.
Why is this not the correct declension?
For nouns which end by -кa, -а is replaced by -и:
The sound shifts кы > ки, гы > ги and хы > хи date back to the 12th or 13th century and were unconditional, making кы, гы and хы prohibited sequences in Russian phonotactics. They only occur in a handful of mostly Turkic loanwords, such as хычин and акын, some toponyms, and гы, a slang onomatopoeia for crass laughter. This is a different phenomenon from the purely conventional spelling preference for жи and ши despite the vowel being technically [ы].
Thus an older genitive form of рука was indeed рукы rather than the modern руки, but the form *Америкы never existed because the sound shift predates Columbus.
ыafterк. The only example which is not a loan word that I can think of isкыш!