Travel from syd, transiting HK, then to Beijiing staying for 58hours

Alice, if you travel like SYD-HK-Beijing (72 hours) - a third country or region rather than HK, you will qualify for the 72 hour free transit in Beijing. No need to apply for an entry permit then. You need to inform the airlines that you want to use the 72 hour free transit in Beijing when boarding the plane in HK and after arriving in Beijing, go to the transit counter to apply for the 72 hour free transit program.