The total carbon emissions for a flight from New York, New York to Sydney, New South Wales is 3,722 lbs CO2.

This is equivalent to 1,688 kg CO2e or 1.69 tonnes of carbon dioxide equivalents.

With radiative forcing in effect, the carbon emissions
may increase by 2.7 times, so the CO2 equivalents would then
be 10,050 pounds, equivalent to 4,558 kilograms or 4.56 metric tonnes.

These calculations are based on the distance from New York, NY to Sydney, Australia which is 9,934 miles or 15,988 kilometers.

This trip is a long haul international flight.
The calculation includes an assumption of a 79.7% load factor with 346 seats on the B747-400 and 261 seats on the B767-300ER.

All calculations are for the carbon emissions per passenger
on the flight (one-way). Depending on the length of the flight,
there are assumptions on the load factor and number of seats,
so you could multiply by the load factor and total number of
seats to estimate the total number of passengers on the plane,
thus computing the total carbon emissions for the entire flight
(all passengers combined). CO2 emissions in air travel vary by
length of flight, calculated as grams of CO2 per passenger kilometer.
This is the data used to estimate flight emissions,
originally from UK DEFRA:

Domestic = 158 gCO2/pkm assuming 0.65 load factor

Short haul international (less than 3700 km) =
130.4 gCO2/pkm assuming 0.65 load factor

Long haul international = 105.6 gCO2/pkm assuming 0.797 load factor

So based on whether the flight is domestic or international,
you can multiply the flight distance in kilometers by the appropriate
factor for grams of CO2 per passenger kilometer, then do appropriate
conversions to kilograms or pounds if necessary. This gives you
the carbon emissions for a single passenger. Then you can take into
account the load factor and total number of seats to sum up the
total carbon emissions for a plane full of passengers if needed.