MS PE (portable executable) format is based on COFF. So /Tx68-coff means PE32 format, /Tamd64-coff means PE64. The asm means that will be output an assembler file instead of an object.
amd64, and not x64, because the actual 64bits architecture was developed by AMD, then adopted by INTEL. The 64 bits approach of INTEL passed through the ALPHA processor (patent acquired by INTEL from DEC (Digital Computer Corporation)) then to ITANIUM INTEL processor, that have a completely different HW architecture.
The genial semplification invented by AMD to extend to 64bits the standard x86 architecture become a de-facto standard in very short time (basically because both instruction sets could be used in a mixed form allowing 64bits use in preexistent codes and systems with small modifications) forcing INTEL to buy rights to adopt the standard for its processors.
The ITANIUM is used on big machines and servers, but had not so much fortune on PC because all existend binary code could not be used.
Last note about the PE (alias MS-COFF) it is not compliant with the standard COFF format because of the different interpretation of bytes offset in the code (so a pure COFF object file could be linked with MS-COFF objects, but the pointers will be wrong and, obviously, the proggram will crash
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