Get hash values, then extract authors from that values (arrayes of hashes) using Enumerable#map
:
books = {
"Harry Potter" => {"Genre" => "Fantasy", "Author" => "Rowling"},
"Lord of the Rings" => {"Genre" => "Fantasy", "Author" => "Tolkien"}
}
authors = books.values.map { |h| h["Author"] }
# => ["Rowling", "Tolkien"]