Show a webform input if user selects certain option from select list?
Update to a newer version of Webform where webform_conditional has been merged.


  Description: This modules enhances the existing Conditional Rules of
  the Webform Module. It adds the ability to make components dependent
  on select components(i.e. listboxes, radio buttons, and checkboxes)
  that appear on the same page.
  
  Important As of Webform version 7.x-4.0-alpha2 this module has been merged into Webform and is no longer necessary. The 7.x-2.x
  version of this module handles this upgrade. See: #1616376: Create
  Migration to Webform 4.x


Then when you make a webform node you will have additional local task labeled conditionals. Once you've added form fields to the webform -- you can set conditions using the administrative form found there.