Cant get into my external Hard Drive

I am running a windows 7 computer with a SSD and internal hard drive set up.  I have an external hard drive plugged into my USB port but when I open my computer I cant access it.  I thought it would have shown up as a letter drive or at least I could see it in my devices/removable storage.  Neither populate.  

When I right click on my computer, it does show up in "device manager/disc drives" and disc management disc 2 (I think).

so, I am clearly not telling it what I need it to do.  When I go into the top box in disc management and try to assign it a letter path it is all grayed out. 

Please share with me wth you think my next step is in setting this up on my computer.  I would like to assign it a letter path or at least be able to pull files out or drag them in.

OR.... have I lost my files and is the disc empty?   
I am posting a pic of my disc management.  Thank you in advance for any thoughts on this I am sure easy problem to correct.

You need to assign drive letters to the partitions. This can be done through the command prompt of diskpart. Make sure you are working with the correct volume numbers. You can tell by the partition sizes.

I have not used Aoemi Partition assistant to change volume letters but you can do it graphically as shown here. Click on the partition of the Disk and then follow the steps.

May be your external hard drive is corrupted or gone something wrong. If you want to pull out your files from disk then you need to take this for data recovery.