Final answer:
AMD64 and EM64T are the two hybrid processor technologies that can natively handle both 32-bit and 64-bit operating systems. Itanium and IA64 do not support 32-bit operating systems in the same way and are different architectures.
Step-by-step explanation:
The two technologies that are hybrid processors capable of handling both 32-bit and 64-bit operating systems natively are AMD64 and EM64T.
AMD64, now commonly known as x86-64, is an architecture developed by AMD. It was one of the first commercially available 64-bit architectures that was backward-compatible with 32-bit architecture, allowing the use of both 32-bit and 64-bit operating systems and applications. EM64T, standing for Intel Extended Memory 64 Technology and also known as Intel 64, is Intel's implementation of AMD64 and similarly supports both 32-bit and 64-bit operations.
The options Itanium and IA64 are both related to a different architecture known as Intel Itanium Architecture, which is not designed to natively support 32-bit operating systems in the same way AMD64 and EM64T are.