please help me sovle this question!

"rather" implies a negative value judgement whereas "fairly" does not.
The house was rather large (implies slightly too large)
The house was fairly large (neutral description...."fair" imples "justifiable")

Be careful about 1. Local variations 2. Writing off the top of your head. In BrE "rather good" can mean "excellent", while "fairly good" can mean "merely or moderately good".

Good point. "Rather" can be associated with a preference .
In the (upper class) exchange....."Would you prefer a whiskey ?"...."Rath - er !" Thus there is a cultural context of its usage which can invert a negative value judgement by stressing the preference factor as in the phrase "rather good". (I am reminded of the current fad for reversing "wicked").

I am a middle-class British (English) person, and I know whereof I speak. In British English, "rather" is always an intensifier. I don't know where you got the idea that it could be otherwise. It generally means decidedly, notably, conspicuously, memorably, etc.

She's rather pretty - she's unusually or outstandingly pretty.
It's rather hot today - it's unusually or outstandingly hot today.

This roast beef is rather good, that tramp is rather smelly, that coat is rather expensive, my house is rather small, etc.

On the other hand, "fairly" is faint praise. If coupled with a positive adjective generally mild criticism is implied - this roast beef is fairly good (it's only just edible) - she's fairly pretty (she's not a dog, but only just)

My house is fairly small (it's a bit small)

Sometimes you can make people think that you actually know something about English, Contrex. That must be those times when you think, eh?

I agree it is an intensifier when used with another adjective. The OP simply need to know that "rather" is more extreme than "fairly".

They can be synonymous in some contexts eg. A rather (fairly) poor attempt at typing 'solve'.