Final answer:
The most likely cause is that the motherboard UEFI/BIOS doesn't support hardware assisted virtualization.
Step-by-step explanation:
The most likely cause for the technician being unable to install virtualization software on the host computer is that the motherboard UEFI/BIOS doesn't support hardware assisted virtualization. Hardware virtualization requires support from the motherboard's UEFI/BIOS in order to enable the virtualization features of the CPU. Without this support, the virtualization software cannot be installed.
In contrast, the other options mentioned would not cause the inability to install the virtualization software. Insufficient physical memory on the host would affect the performance of the virtual machine but not prevent software installation. The absence of an auxiliary hard drive would only affect where the VM files are stored, but it wouldn't prevent the software installation. Similarly, the absence of multiple core processors in the CPU would only impact the performance of the virtual machine but not prevent software installation.