The phrase "put the can" can be used in a variety of situations, from placing a can in the recycling bin to kicking a can down the street. However, there are plenty of alternative phrases you can use depending on the context. For example, you can "dispose of the can," "deposit the can in the bin," or simply "throw away the can." Alternatively, you can describe someone as "tossing the can," "placing the can gently," or "carefully setting down the can." Each synonym offers a unique nuance to the action, so choose the one that best suits your intended meaning.