What Do Two Question Marks in a Row in a Ternary Clause Mean?

It is simply a nested ternary statement. Clearer by adding parentheses:

number == null ? (required ? 1 : 2) : 3;

what would the inputs need to be for 2 to be returned?

number = null and required = false

This is why it’s always a good idea to explicitly add parentheses, so the intent is clear at a glance :

Integer val = number == null ? (required ? 1 : 2) : 3;