formatting an external hard drive

Try Disk Utility for Mac: Erase a volume using Disk Utility

Drive Partition and Format

1. Open Disk Utility in the Utilities' folder.
2. After Disk Utility loads select the new WD drive (out-dented entry with the mfgr.'s ID and size) from the side list.
3. Click on the Erase tab in the Disk Utility toolbar. A panel should drop down.
4. In the drop down panel set the partition scheme to GUID. Set the Format type to Mac OS Extended (Journaled.)
5. Click on the Apply button and click on the Done button when it is activated.
6. Quit Disk Utility.

You may be presented with an alert asking if you want to use the new drive as the Time Machine backup drive. If that is the purpose for the new drive then click on the Yes option's button.

i wish to attach to my synology router w usb 3 and a 4tb port hdd

for time machine

have 4 macs 2 w high sierra, two iMacs running 10.9

do i partition 4 ways one for each mac? or single partition as above .

ok for the new file system?

thanks

Have a look here please: Format a Mac's Drive With Disk Utility (OS X 10.11)