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if you are trying to avoid learning #inject (which you should not do...)
words = ['cat', 'dog', 'snake', 'dog']
count = Hash.new(0)
words.each {|word| count[word] += 1}
count.sort_by { |k,v| v }.last
but if I read this answer before, now I would know nothing about #inject and man, you need to know about #inject.