What Ketan is trying to say is correct. An image cropped by a factor of 2 is equivalent to an image obtained with the same lens (and FL) with a 2x TC. E.g., the "effective" f-number is doubled.
This consideration assumes and requires that all images are compared at the same size (e.g. printed to the same size, or viewed on the same monitor). This point is crucial.
This is how the effect of cropping can be understood:
When we take an uncropped image, for example at 200mm f2.8, the exposure is the amount of light captured by the entire sensor and divided by the image surface area (light per unit area).
A 2x crop from this image obtained with the 200mm f2.8 lens has one-quarter of the light captured by the sensor. Thus, when the cropped image is viewed or printed at the very same size as the uncropped image, then the exposure, which is light per unit surface, is reduced fourfold or by two stops, as if the cropped image was taken at 400mm f5.6.
In other words, if we take an image at 200mm f2.8 and make a print, then cut one quarter of that by scissors, the exposure on the small crop (cut) wouldn't change. However if we take this crop, cut by scissors, and enlarge it somehow and reprint to be of the same print size as the original 200mm f2.8 image, then the enlarged print should be equivalent to 400mm f5.6.
Equivalent here means that an image of the same subject taken from the same point with a true 400mm f5.6 lens, and printed to the same size as above should be indistinguishable and should display the same amount of noise as the enlarged crop from the 200mm f2.8 image.
A 2x TC acts by projecting on a sensor one-quarter of the light captured by the "naked" lens; thus, the exposure is reduced by two stops, and the f-number of the lens is doubled.
The above considerations ignore any optical effects of teleconverters on the image quality. Thus, the image quality at the pixel level can be different in the images that we refer to as "equivalent" here. E.g. a TC can likely add chromatic aberrations. Whether this is going to be visible in the respective final images can be difficult to tell. I don't think there's an established consensus on whether cropping or using a TC is the preferred method. This can much depend on the post-processing skills of photographers.
