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The problem may be with the camera itself, or with the Mac.
Try testing the camera by connecting it to a different Mac or PC.
If it is recognised ok there, then the problem is with your own Mac.
If the camera cannot be recognised on any computer, then the camera itself has a fault.
Also, if you are using software for the transfer, try accessing the camera directly through Finder, and check if you can manually copy the video files to the Mac.