Correct Answer: To create a volume group with 8M extends and a logical volume with 50 extends, format it as ext4, and automatically mount it under /mnt/data with a size between 380M and 400M, follow these steps precisely: 1. Use fdisk to create a partition on the desired disk. 2. Use partprobe to let the kernel know about the partition table changes. 3. Initialize the partition with pvcreate. 4. Create a volume group with a physical extent size of 8M using vgcreate. 5. Create a logical volume with 50 extents using lvcreate. 6. Format the logical volume with ext4 using mkfs.ext4. 7. Create the /mnt/data directory using mkdir. 8. Edit /etc/fstab to mount the logical volume automatically by adding '/dev/vg1/lvshare /mnt/data ext4 defaults 0 0'. 9. Use mount -a to mount all filesystems mentioned in /etc/fstab. 10. Verify with df -h or lsblk. The detailed commands are: 1. fdisk 2. partprobe 3. pvcreate /dev/vda6 4. vgcreate -s 8M vg1 /dev/vda6 5. lvcreate -n lvshare -l 50 vg1 6. mkfs.ext4 /dev/vg1/lvshare 7. mkdir -p /mnt/data 8. vim /etc/fstab and add the line '/dev/vg1/lvshare /mnt/data ext4 defaults 0 0' 9. mount -a 10. df -h Ensure the logical volume is sized between 380M and 400M, which 50 extends of 8M each will satisfy (50 * 8M = 400M).