How do quaternary ammonium salts catalyse SN2 reactions?
Trimethylbenzylammonium chloride is in this reaction a good example of a phase transfer catalyst. It first forms the trimethylbenzylammonium cyanide in aqueous phase (or on the surface of solid phase) which is soluble in the organic phase. Because of the polar nature of the cyanide ion it is not going to be heavily solvated by organic solvent (in this case benzene) molecules so the result is 'naked' cyanide which is highly reactive. This reacts with the substrate forming, in this case, the cyanodecane and trimethylbenzylammonium bromide. The trimethylbenzylammonium bromide is then free to migrate back to the aqueous phase and exchange anion to reform trimethylbenzylammonium cyanide. Most phase transfer reactions benefit from vigorous stirring to accelerate the exchange between the phases. 

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