Write all possible two-digit numbers using the digits 4 and 0. Repetition of digits is allowed.

We are required to write 2-digit numbers using the digits 4 and 0, where repetition of digits is allowed.

The digit 0 cannot be at the ten's place because that would make the number only 1-digited.

Keeping 4 at ten's place, the 2-digit numbers are 40 and 44.

Hence, all possible 2-digit numbers are 40 and 44.