Mohamed52,
Linux Mint is derived from Ubuntu. The two are closely related.
I imagine the install routine for Linux Mint will be more or less the same as for Ubuntu.
My recent experience with multiple installs of Ubuntu required a slight deviation from Brian K's method.
Starting from scratch, the Ubuntu install guide found in the TBI KB is helpful reading:
https://www.terabyteunlimited.com/kb/article.php?id=279
The guide was updated for Ubuntu 15.04 and BootIt BM but remains broadly relevant to Ubuntu 20.04 and BootIt UEFI (BIU).
Edit: TBI have made a similar install guide for Linux Mint:
https://www.terabyteunlimited.com/kb/article.php?id=281
The process I used to successfully install Ubuntu 18.04.5 and Ubuntu 20.04.1 with BIU follows...
(1) In BIU use Partition Work to create the partition into which Linux Mint will be installed.
I made it 60000 MiB. For file type select "Linux Native".
No need for an extra Swap partition; a swap file will be created in / (root) partition by default during installation.
(2) Go to BIU's "Boot Edit" screen.
=> Add -- to add a new boot item for Linux Mint
"Boot" field -- direct this to the partition you made for Linux Mint
"Boot File" field => hit "Browse" button. Direct it to same / (root) partition where Linux Mint will be installed.
Notice will appear saying "Unable to mount file system" => OK.
Use OK buttons to click out of the Boot Edit screen.
(3) At BIU home screen hit Resume.
(4) At BIU's boot screen select the boot item made for Linux Mint and try to boot from it.
The boot attempt will fail. That's expected. There's no OS yet and boot loader hasn't been installed yet either.
(5) Insert your installation media. Best to flash .iso install file to USB stick.
Put stick into USB port and reboot into it.
(6) When the install procedure reaches the "Installation Type" screen choose "Something Else".
In the upper field of the next screen find the partition created for Linux Mint.
Double click its line to select it as partition to install to.
Select file system (ext4 is good for most purposes). Check format option. Select mount point as / (root). Hit OK.
Below the upper field is a wide button labelled "Device for boot loader installation".
Select the same partition as selected above for / (root) ***
***This is the point of difference between my method and Brian's. When I directed installer to put boot loader into EFI partition as Brian suggests the result was a mess. Cannot recall its exact nature but was bad enough for me to delete everything (including new ubuntu.nnn directory added to ESP) and start again using this method. Which works.
Now carefully check the options you've selected.
Make sure correct partition for install has been selected, and that existing OS and data partitions will not be overwritten.
Hit the Continue button and proceed with the install.
After installing reboot. Machine will boot directly into new OS - you won't see BIU boot screen.
You will need to reactivate BIU at next reboot.
Reboot into BIU.
(7) BIU boot screen will have listing for boot item you created plus a newly created boot item.
For Ubuntu installs the new boot item created by the installer is labelled "ubuntu". Maybe you'll see "LinuxMint" instead.
Enter BIU "Maintenance" => Boot Edit screen.
Select the boot item made earlier for Linux Mint => Edit
Boot File => Browse
Drill down through this path in / (root) partition:
\boot\grub\x86_64-efi\grub.efi
Click OK to save your work and return to BIU home screen.
Hit Resume => takes you to BIU boot screen presenting list of boot items to boot from.
Check that the boot item you created boots to Linux Mint.
Later you might check the "LinuxMint" boot item that was created during the install process via BIU Boot Edit => Edit.
Its path to boot loader will be different but still works.
For my Ubuntu installs the extra boot item created by installer is setup to look for boot loader in EFI System Partition (ESP).
Path for boot loader file is something like: \EFI\ubuntu.nnn\grub64.efi