It's not really convertable because they are measures of different things. One is a fuel economy (how far a vehicle can travel on a certain amount of fuel) and the other is an emission standard (how much mass of pollutant is emitted per amount of energy consumed). It makes no sense to basically ask if a car gets so many miles per galon, what is its fuel economy in g/kwh?
To do any kind of conversion, you'd need to account for the energy density of the fuel and so forth. From a practical point of view, you also need to know the efficiency with which the vehicle converts the fuel energy to usable energy, and the efficiency with which the car traps pollutant mass (catalytic converters, filters, etc.). I.e., you need more information.
Boiled to its basic SI units, g/kwh is s2
and mpg is m-2
. Just from this fact alone tells you that you need more information to do any kind of conversion.
By the way, an interesting tidbit on the units of fuel economy, which has units of inverse area: https://what-if.xkcd.com/11/