Welcome to the community, Scott!
I believe that this is something that you'd need to contact the DVR security system manufacturer's customer support. However, if it's stated in the manual and the specifications of the DVR that the maximum HDD capacity that it can support is 4 TB, then it's highly unlikely that a 6 TB hard drive would work.
Either way, the people who would point to the right answer and solution are the manufacturer's tech support. Make sure you get in touch with them.
Best of luck!
SuperSoph_WD