Travel by Car: The driving distance between Mannheim and Mostar is about 1.400 km, and travelling time is about 13 hours. Recommended route goes trough Croatia, Slovenia, Austria via highway where tool fees apply. In Germany highways are free of charge.
Travel by Bus: If there are direct buses from Mannheim to Mostar, timetable and price tickets for buses can check here. Alternatively it is possible to travel via Sarajevo or Zagreb in Croatia.
Alternative ways of travelling from Mostar to Mannheim:
Travel by train: From Mostar there is a possibility to travel by train to Zagreb (via Sarajevo), and then continue with international train to Mannheim (via Munchen).
Travelling by train from Mostar to Mannheim is much slower that travelling by bus or car, as trains in Bosnia and Herzegovina and Croatia are very slow. More information for travelling by train in Bosnia and Herzegovina you can check here.
Travel by plane: There is no direct flight, but there is option to fly to Sarajevo.
Map with buses from Mostar: