Why does an Avro RJ85 have four engines?
It was originally the BAe 146 and was designed for operating out of city airports such as London City Airport.

The main reason is for noise abatement. Back in the 80s, four high-bypass turbofans made a lot less noise than two contemporary engines.

Climb performance is also fantastic.  it can climb safely from most airports using much less than full power which helps keep the noise down and provides high safety margins when operating near built-up areas, for example if an engine fails on take-off.