$ sudo apt-get update
$ sudo apt-get install libx264-142 

libx264-142 is installed in your system.

Make ensure the libx264-142 package were installed using the commands given below,

$ sudo dpkg-query -l | grep libx264-142 *

You will get with libx264-142 package name, version, architecture and description in a table

libx264-142 package basic information: