Hi,
I just checked my machine, and my external USB 3.0 HDD appears...
Was your drive attached and plugged in when you started the computer ?
I don't know if it will work if it is plugged after the machine boots... The repair works different than regular windows under some conditions like that..
If you can not get the external drive to appear, you may need to use one of the other drives if they have enough room...
I'm glad you posted that picture though... I forgot to mention something about installing Windows..
It is best to unhook ALL extra drives when doing the installation... Except for a CD\DVD drive...
This is because Windows will store boot files on any drive that is attached... If you should then remove one of those drives in the future, Windows will not boot...
From your picture, I can not determine which drives are actually "Drives" or just "Partitions" on a drive..
Unfortunately that is the way windows does things...