I have two external hard drives connected to my Mac with OS X El Capitan. I am using one of the external hard drives with Time Machine as the back up hard drive only. The second external hard drive I use to store my many photos. How can I get Time Machine to back up both the internal Mac hard drive and the external hard drive storing my photos? Right now, it will only back up the Mac internal hard drive. I need it to also back up the external hard drive.
Yes - you should be able to backup your external drive with the photos by removing it from the "Exclude" tab in the Time Machine pane in System Preferences (in this case the external drive is FCPX):
As Nancy Casas also mentioned, a disk in gray will have to be reformatted for Mac, while one in black will not.
You should be able to back up any external HD, if it's formatted for a Mac.
By default, all externals are excluded and shown in the exclusion list in Time Machine Preferences > Options.
If you see it there, in black, just select it and click the minus sign at the bottom.
If you see it in gray, that means it's not formatted for a Mac, and Time Machine can't back it up. You'll have to copy the data elsewhere temporarily, reformat the drive, then remove it from the exclusion list.