Here is another way of doing it "manually lol"... You do each to iterate of over the nested arrays [[0],[1],[2]], then you iterate over each nested array and use include
ary[pos].include?(x) with AND between all three nested arrays to find intersecting value, It will be slow, but handy if you want to add more conditions .
user> ary = [ [1,2,3,4], [3,4,5,6], [4,5,6,8] ]
=> [[1, 2, 3, 4], [3, 4, 5, 6], [4, 5, 6, 8]]
user> ary.each { |f| f.each {|x|
puts "#{x}" if ary[0].include?(x) && ary[1].include?(x) &&
ary[2].include?(x) }}
4
4
4
or simply,
2.1.2 :003 > ary = [ [1,2,3,4], [3,4,5,6], [4,5,6,8] ].inject(:&)
=> [4]