Multi class classification can be considered as a regression problem, where the model predicts the probability of each of the classes independently. For example, in your case, it means the model would give 4 outputs, one each for right hand, left hand, right leg, and left leg.
There are multiple models that could be used for this. One option is to use a neural network, where you put sigmoid as the last layer. Another option is to use mvregress function.
