If you want to preserve EAX and the upper half of EBX:
rol eax, 16
mov bx, ax
rol eax, 16
If have a scratch register available, this is more efficient (and doesn't introduce extra latency for later instructions that read EAX):
mov ecx, eax
shr ecx, 16
mov bx, cx
If you don't need either of those, mov ebx, eax
/ shr ebx, 16
is the obvious way and avoids any partial-register stalls or false dependencies.
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