If that screenshot is from your own computer, then you’ve installed Manjaro in legacy BIOS mode, not in UEFI mode.
If you’re going to use legacy BIOS mode on a GPT-partitioned drive, then you need to create a special partition of type
bios, about 2 MiB in size, marked with the
boot flag, and not formatted with any filesystem. This partition will then be used by GRUB to store its
core.img stage, or else GRUB will overwrite the partition boundary right behind the GPT headers.
Apparently you do not have a partition of type
bios on your drive, and therefore the GRUB installer throws up an error.
That all said, if you have Windows 10 on your computer, then odds are that Windows will have been installed in UEFI mode. And as such, you need to install Manjaro in UEFI mode too. You already do have an EFI system partition.
You will have to enter the UEFI firmware settings first and disable legacy BIOS “CSM” mode. Then, boot up from the Manjaro USB, open up a terminal window, use
su - to become root, and then issue the following commands…
mount /dev/sda6 /manjaro
mount /dev/sda1 /manjaro/boot/efi
grub-install --recheck --no-rs-codes --modules="part_gpt part_msdos" --efi-directory="/boot/efi" --target="x86_64-efi"
After this, it should be safe to properly reboot your computer.