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I suspect that your portable HDD is not recognized because it has not been partitioned or formatted. You have to get into computer management and follow the following instructions:

To create and format a new partition (volume)
Click to open Computer Management. If you are prompted for an administrator password or confirmation, type the password or provide confirmation.

In the left pane, under Storage, click Disk Management.

Right-click an unallocated region on your hard disk, and then click New Simple Volume.

In the New Simple Volume Wizard, click Next.

Type the size of the volume you want to create in megabytes (MB) or accept the maximum default size, and then click Next.

Accept the default drive letter or choose a different drive letter to identify the partition, and then click Next.

In the Format Partition dialog box, do one of the following:

If you don't want to format the volume right now, click Do not format this volume, and then click Next.

To format the volume with the default settings, click Next.

Review your choices, and then click Finish.

Note
When you create new partitions on a basic disk, the first three will be formatted as primary partitions. Beginning with the fourth, each one will be configured as a logical drive within an extended partition.