I would say to hold an enquiry means to investigate a certain case in an official way, oftentimes on government level.
Maybe, Alan will give us more details. Here is the sentence you are referring to:
The government has decided to hold an enquiry into the latest financial scandal.[YSaerTTEW443543]
TOEIC listening, photographs: In the city[YSaerTTEW443543]
Just to add to what Torsten has already written. If there is something that is of great concern/worry to the public, the government will start/hold an enquiry (a sort of investigation) to try to find out what has happened and different people will be asked questions and be interviewed in the hope that the truth will be found. In the end the group of people who have been making the enquiry will publish a report. Enquiries are held for example if there has been a terrible plane crash to find out why it has happened.
Why can’t we use ‘examination’ or ‘evaluation’? The meanings are similar and both are used in the field of economy as well or am I wrong? In which cases would I use those vocabularies?
I think the key to the expression is ‘hold’. We don’t usually ‘hold an examination or an evaluation’. More appropriate with these two nouns would be ‘carry out’.