Further (additional) to others above, and keeping it simple, the...

Further (additional) to others above, and keeping it simple, the company keeps track on tax paid to the ATO on their profits and BAS statements, this is done through the "Franking Account" in their accounting system. So based on the balance of franking Credits in that account, and the dividend amount declared, the company can determine the franked amount / %, and apply it at the time of declaring interim & final dividend. If the account is empty, a declared dividend would be "Unfranked".

The Franking account gets larger with Tax paid, and if they receive franking credits on dividends they receive from their investments (if any), and reduces when they pay Credits out in franked dividends to shareholders.