This will match a password that has at least 2 numbers, 2 lower case letters, 2 upper case letters, and 8 to 20 characters:
^(?=.*?\d.*?\d)(?=.*?[a-z].*?[a-z])(?=.*?[A-Z].*?[A-Z])[\da-zA-Z]{8,20}$
If you just want to check if it has multi-case and digits:
^(?=.*?\d)(?=.*?[a-z])(?=.*?[A-Z])[\da-zA-Z]$