list.group_by(&:capitalize).map {|k,v| [k, v.length]}
#=> [["Master of puppets", 3], ["Enter sandman", 2], ["Nothing else matters", 1]]
The group by creates a hash from the capitalized version of an album name to an array containing all the strings in list that match it (e.g. "Enter sandman" => ["Enter Sandman", "Enter sandman"]). The map then replaces each array with its length, so you get e.g. ["Enter sandman", 2] for "Enter sandman".
If you need the result to be a hash, you can call to_h on the result or wrap a Hash[ ] around it.