Alphabetically sorted numbers
sort_by cleans this up quite a bit, and avoids the unnecessary conversions to and from strings:

def sort_alphabetically(numbers)
  alphas = %w(zero one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen nineteen)
  .map.with_index {|x,i| [i, x]}.to_h

  numbers.sort_by {|x| alphas[x]}
end


Notes:


Point on naming: use a verb, or else a noun describing what the function returns: sort_alphabetically or alphabetically_sorted. I know technically alphabetically_sorted isn't a noun, but I see it as an abbreviation for alphabetically_sorted_list, which is too verbose.
If speed matters, you should compute the hash outside the function, so it's only done once.