I think car brakes will break on all wheels simultaneously (although more braking force may be applied to the front wheels). Also, the engine should generally not transmit any power to the wheels when you are braking.
But sure, if you want to try and break a car (or any machine for that matter) you can try to push down the gas pedal and the brake simultaneously (I don’t know what the electronics in modern car would do in this case). In such cases usually the weakest element in the chain will break/deform or similar.
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