I read about APS-C sensors EOS DSLRs, that if the focal length is 300mm and as the image ratio is 1.6 then the 300mm x1.6 = 480mm focal length. So if I add a 1.4x teleconverter to 300mm lens so I should be getting 480mm x1.4 = 672mm focal length?
The focal length of the lens system with a teleconverter will be 300mm (from the lens) * 1.4x (from the converter). This will give you a lens system with a focal length of 420mm.
Cropping of the image by the sensor from the full field of view to the APS-C size doesn't change the focal length... it just gives you the same field of view if you had a lens that was 1.6x longer on a full frame camera. This distinction is key when you start looking at the depth of field calculations and the like.
The focal length of the lens does not change if you go into photoshop and crop the image to a smaller size. Nor does it change when you use a sensor that is smaller than the image circle projected.
In this case, the field of view would be the same as that of a 672mm lens on a full frame camera (the lens system focal length * 1.6).