Newer versions of Adobe Acrobat Reader DC (currently at 23.006.20360) have changed both the wording and the function within Preferences. Instead of unchecking the option to open the Tools Pane by default, the application will now remember whether it was shown or hidden previously.
Before you change your preferences, open Acrobat Reader and from the Menu Bar and navigate to View > Show/Hide > Tools Pane to hide it accordingly.
More recent iterations of of Acrobat Reader DC will still display a set of icons near the right side of your PDF document after you hide the Tools Pane. However, you can easily hide them by clicking on the icon at the bottom-right that allows you to Hide Task Pane.
Once that is done, use the Menu Bar (or press Ctrl+K) to select Edit > Preferences and in the subsequent window highlight Documents on the upper-left. Check the box to Remember current state of Tools Pane and then select the OK button.