noMethodError : each no String

So, the main issue I see is this part of your answer:

if contact["phone_number"].size>0
  contact["phone_number"].each do |phone_number|
     puts "Phone: #{phone_number}"
  end
end

I'm not sure why you did that, but you don't need to.

Firstly, this is a very simple array, consisting of 2 hashes. You can see the data, which shows the phone_number key has a value in each case. So you don't need to check if it exists - but if you did want to anyway, just typing this would be sufficient:

if contact["phone_number"]
   # Do something
end

Secondly, you are trying to iterate through the phone_number. by typing contact["phone_number"].each do |phone_number|

This doesn't work since the phone_number is a string, not an array. To out put the phone number all you need to do is:

puts "Phone: #{contact["phone_number"]}"

Therefore, the final code would look something like:

contact_list = [
  {"name" => "Jason", "phone_number" => "123"},
  {"name" => "Nick", "phone_number" => "456"}
]

contact_list.each do |contact|
  puts "Name: #{contact["name"]}"
  puts "Phone: #{contact["phone_number"]}"
end