Please consider the following steps to update ArcGIS 10.2 for Desktop, ArcGIS 10.2 for Server and ArcGIS Engine.
Note: In order to get the latest Esri patches also have a look at http://support.esri.com/en/downloads/patches-servicepacks/.
Download Esri patch finder
Please use the Esri patch finder tool from the link above to check your current installed versions of Esri patches.

Download Esri patch finder
Download Esri patches
Compare the result of the patch finder tool with the patches provided from Esri, download the missing patches and install them on your system.
Note: Use the filter function to find the latest patches of an Esri component.

Filter function for searching Esri patches
Installation of an ArcGIS for Desktop Patch
Whenever an ArcGIS for Desktop Patch is to be installed, be aware to shut down the component services (WebOffice plot, WebOffice ePaper, WebOffice export) in order to run the upgrade successfully. Therefore, open the component services, navigate to COM+ Applications and shut down the respective component services via context menu.
Note: After the successful installation of the patch, you will have to restart the component services!

Shut down the component services before installing an ArcGIS for Desktop patch