Are you both using the same licensed copy of FileMaker? FMI has built in a system to rigidly stop more than one copy of any license number from using the same network at once.
Even if you have separate licenses, aslo check that more than one copy isn't installed on one of the machines.
If you still have this problem with separate fully-licensed copies of FMPro/Adv, it's probably a problem with multiple External/FileMaker Data Sources in one or more of your files. If your files have comflicting or multiple IP references to each other, this conflict will trigger as soon as a copy of FMPro tries to open a 2nd connection to the same file via more than one IP path. See menus:
File > Manage > External Data Sources
If you have multiple files, you may need to check this in all of your files. The conflict doesn't have to be within the same file to cause this error.