How does HOMER calculate emission, especially carbon dioxide?

If the system you are modeling consumes fuel, HOMER calculates the total annual carbon input by multiplying the fuel consumption by the carbon content of the fuel.  It assumes that all that carbon gets emitted as either unburned hydrocarbons, CO, or CO2.  You enter the emissions factors for unburned hydrocarbons and CO, so HOMER can calculate how much of the total carbon gets emitted in those two forms.  The rest gets emitted as CO2.

Typically only a tiny fraction of the carbon gets emitted as hydrocarbon and CO, so nearly all of it gets emitted as CO2.  If you are interested only in CO2, you should set the UHC and CO emissions factors to zero.  Note that 3.67 g of CO2 contains 1 g of carbon.  So ignoring UHC and CO emissions, the system will emit 3.67 g of CO2 for every g of carbon in the consumed fuel.

Please look up "calculating emissions" in the index of HOMER's help file for more information.