"Putting it away" is a common phrase that means to store something in its proper place. There are several synonyms that can be used to convey the same meaning. For example, "storing" can be used to describe the act of putting something away for later use. "Putting it up" is another phrase that can be used to describe the same action. "Depositing" can be used to describe the act of placing something in a secure location, while "placing" and "arranging" can also be used to describe the act of organizing things in their appropriate places. Ultimately, the goal of all these synonyms is to help you keep your space clean and organized.