I am on Linux Mint 19.03.
I want to set a 64 bit Windows 10 into a virtual machine, however it does not prefer me to choose a 64 bit of any windows version, as shown in the figure.
Anybody here to help me to understand why it is so?
Your PC can only virtualize 32 bit OS'es because you have not enabled the virtualization features in your BIOS.
Giving exact instructions here is difficult, as every BIOS is a little different.
The settings should be called 'Intel Virtualization Technology', 'AMD-V' or similar and appear mostly in the CPU settings.
Regarding the Hyper-V comment: Hyper-V is a Windows virtualization technique and does not exist on linux machines.