Multi window functionality allow the user to run and use multiple applications at the same time. This functionality is not available for Samsung Galaxy Core but thanks to an XDA user, you can get this functionality on your phone.
The only requirement is that you must have CWM or TWRP for the Samsung Galaxy Core. Then download the multi window file from here and put it into the root folder of your Galaxy Core.
Boot into recovery mode. For that press and hold down volume up button till the phone boots into recovery mode. Then select multi window file and flash it.
That is it. You now have multi window on your Samsung Galaxy Core android phone.