Why not jeji instead of jejiho
when do you use muze instead of muz?
Here muže is the accusative form of the word muž, it's required by the preposition na.
You can see the noun's complete declension here: https://en.wiktionary.org/wiki/mu%C5%BE#Czech
Also read the tips and notes: https://www.duolingo.com/skill/cs/Prepositions-A