How to merge two partitions on external hard drive when the "partition" option is greyed out?
To elaborate the answer by @klanomath this is what you must do step-by-step:


get the disk identifier for both disks you want to merge by "diskutil list [disk name]". Choose any of the two disk names, like:

 diskutil list MacBackup



This returns something like

   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:     FDisk_partition_scheme                        *320.1 GB   disk3
   1:                 DOS_FAT_32 MULTIMEDIA              160.0 GB   disk3s1
   2:                  Apple_HFS TIMEMACHINE             160.0 GB   disk3s2


In the IDENTIFIER column, get the disk identifiers for both disks, here: disk3s1 and disk3s2


merge the two disk partitions by "mergePartitions  [format] [new disk name][disk identifier 1]  [disk identifier 2]". If you want to use the "MacBackup3", you would then enter:

diskutil mergePartitions JHFS+ MyMedia disk3s1 disk3s2



The first disk [disk identifier 1] is the only one that diskutil tries to preserve the data for. If it can't because the disk has no resizable data format, it will give a warning message:

The chosen disk does not support resizing.
Do you wish to format instead? (y/N)


Caution! If you enter "y", your data on [disk identifier 1] will be deleted. This is the last chance to abort by "N". If you have backed up the data, you can go on with "y" - your disk partitions will be merged.