Commutative: doing makeup and nails. Non-commutative: starting a car with keys and driving a car.
Work Step by Step
An example of a commutative activity is putting on makeup and doing your nails. The two actions can be reversed (the order does not matter) and thus they are commutative. An example of a non-commutative activity is putting the keys into the car and driving the car. The keys must be put in first to start the car and only then can one drive. Thus the order matters and the two actions can not be reversed (non-commutative).