De or het wereldreputatie?

The correct Dutch article is:

de wereldreputatie

Rule Words ending in -tie and -sie: almost always de. See the rule

How to use wereldreputatie

the wereldreputatiede wereldreputatie
this wereldreputatiedeze wereldreputatie
that wereldreputatiedie wereldreputatie
our wereldreputatieonze wereldreputatie
your wereldreputatiejouw wereldreputatie
every wereldreputatieelke wereldreputatie
which wereldreputatie?welke wereldreputatie?
a big wereldreputatie / the big wereldreputatieeen grote wereldreputatie, de grote wereldreputatie