Hi Aannie,
The prompt asks us to determine the total number of 4-CHARACTER codes (not 4-"digit" codes), so we have to consider each of the possible values that can occur in each of the 4 'spots' of the code. Although the original prompt has a 'typo' in it, we're told that the first two characters are DIGITS (meaning 0-9, inclusive, so 10 options) and the last two characters are LETTERS (A-Z, inclusive, so 26 options). Duplicate characters ARE allowed.
The prompt states that "the same characters used in a different order constitute a different code." For example...
12AB and 21BA are NOT the same code; they're different codes (so they both must be counted towards the total).
GMAT assassins aren't born, they're made,
Rich
760+: What GMAT Assassins Do to Score at the Highest Levels