This upgrade should be very straight forward going from v4 to v6, bypassing v5: 

• Remove old version and install the new one (6.4.2).
• Incorporate a new stylesheet (v4-shims.css) if we don't want to rename icon name references. I believe this is the safest route since many user may have the v4 names being used in pages. If we update all name references via search and replace this new stylesheet will not be necessary
• Done =)
  This page have all the detailed the instructions. https://fontawesome.com/docs/web/setup/upgrade/upgrade-from-v4 
  For peace of mind I would still test the new icons since many of them may have different visuals from the current ones and some adjustments may be still be required pertaining sizes and individual styles;