What is the meaning of the following sentence it is from a book red dragon
He knew the FBI document section would fall on the carving like a rabid mongoose
Fall on in this context is a phrasal verb meaning to be greatly attracted to/by, to notice with interest, to seize eagerly.
It is saying that the FBI would take a keen and immediate interest in the carving. I don't know the book but the FBI interest might arise from suspected tax evasion or smuggling.
The sentence compares the speed that the FBI would follow up on the carving with the speed that a rabid mongoose attacks (a mongoose with rabies).
It's a colourful metaphor to say that he was aware of the great and immediate interest that the carving would attract from the authorities.
https://www.macmillandictionary.com/dictionary/british/fall-on