Area factor is in question here!
The factor is area of cake with 12 inches diameter divide by area of cake with 8 inches diameter
Area = Pi times radius squared
For cake with 12 inches diameter, the area = Pi times 6^2
For cake with 8 inches diameter, area = Pi times 4^2
Area factor = (Pi times 36) / (Pi times 16) = 36/16 = 2.25
He should multiply the recipe ingredients by 2.25