As clinton and I have said you have Tuxera installed which allows you to Write to that drive.
But your problem is coming from that drive not being Mounted. Which if you can't mount it then there is something wrong with the drive. All drives, in good working order and getting the proper power from the USB port, will Auto Mount when connected.
First thing you should do us highlight the Drive Name and Right Click on them and select "Eject Disk" from the menu that comes up. Then Unplug that drive from your Mac. Once you do that to both drives then Restart your Mac to get a fresh clean boot of OS X.
Once the system restarts connect only one of those drive and see if it Auto Mounts.
If it does I suggest you Copy all the important files off it and place those files in a folder on your internal drive.
Then Eject that Disk and connect the other one and again If It Mounts Copy the files off it to your internal drive, That is IF you have enough space on your internal drive.
If one or the other or both do not Auto Mount when connected them there is a problem with either the physical drive in the external enclosure or a problem with the enclosures electronics that is stopping the drive from Auto Mounting. In either case you will have to find out which part has failed, Drive itself or the Electronics.
If just the enclosures electronics has failed you can remove the physical drive from that enclosure and use a SATA to USB Adapter to connect the physical drive to your Mac to get the data off it.