Hi,
Unfortunately LCD screens cannot be repaired they have to be replaced.
Here is a link to the Ifixit guide on how to repair the LCD screen in your camera. Take note in the ''Introduction'' regarding possible breakage using the procedure.
[guide|73648]
Here is a link to just one supplier of the replacement part. It is not a recommendation to use the supplier, it is only shown to give you an idea of the cost of the part. There are other suppliers online, just search for Sony A6000 LCD screen
http://www.ebay.com/itm/Sony-A6000-LCD-Screen-Assembly-Replacement-Repair-Part-/361533175480