To answer this question, the user needs to have knowledge about mainframe hardware and operating systems.

The facility that allows mainframes to be partitioned into LPARs (Logical Partitions) is PR/SM (Processor Resource/Systems Manager).

Option A: z/OS is an operating system used on IBM mainframes. While it provides a range of services for running applications on mainframes, it is not the facility that allows for LPAR partitioning.

Option B: PR/SM is the correct answer. It is a firmware that provides the ability to create LPARs, which are virtualized instances of a mainframe that allow multiple operating systems to run concurrently on a single physical machine.

Option C: Virtual Storage is a feature of the z/OS operating system that provides virtual memory management. It is not the facility that allows for LPAR partitioning.

Option D: Coupling Facility is a hardware component used in parallel sysplex configurations to provide high-speed communications and data sharing between multiple mainframes. It is not the facility that allows for LPAR partitioning.

Therefore, the answer is:

The Answer is: B. PR/SM