which selection will hide/disable the search box?

The selection that will hide or disable the Task View button is "Show Task View button." To hide or disable it, this option simply needs to be unchecked or deselected. Likewise, to hide or disable the Search box, the selection called "Hidden" is used. These selections are typically found within the Taskbar or Start Menu settings in Windows, where toggling "Show Task View button" off will hide the Task View button, and selecting "Hidden" will hide the Search box.