Main vacuum hose on 1995 mercury cougar

What is your question?

I'm trying to find the placement of the main vacuum hoses car starts runs and then hesitate and shuts off after stop and go also seems to not accelerate at all sometimes and get backfire alot fuel indicator is reading 1/4 when it's empty(out of gas)

What makes this problem better or worse?

It's worst when the engine is hot as Nd it's hot outside I have no thermostat

How long has your 1995 Mercury Cougar had this problem?

I bought the car used as maybe 5 months in