Issue encrypting my Seagate drive with Disk Utility on macOS Sierra 10.12.6

You will not be able to do this if the disk is formatted as FAT, FAT32, or EXFAT. In order to encrypt the disk, it has to be HFS or APFS.

You will need to format the disk to HFS or APFS and then you can encrypt. When formatting, there should be an option to format as APFS Encrypted or macOS Extended Encrypted. You can select either one of those or you can encrypt after formatting.

Good luck!

From your screen capture, your external drive has an MBR (Master Boot Record) partition map. To encrypt it, it needs a GPT (GUUID Partition Table) partition scheme. You can then format with the file system format of your choice.

Before encrypting the drive it must be erased first, so if it has data you want to keep, you need to temporarily copy it to another location then copy it back once you finish the erase and encryption process.

For full details, see Encrypt and protect a storage device with a password in Disk Utility on Mac