Chemistry help!!!Watch this thread
This is an acid-base reaction, that is why it comes to protonation. With this clue, you should be able to draw the product.
1.) Bromine is a good leaving group (as the name implies, it like to 'leave' things - stabilises a lone pair of electrons well), as are most of the halogens but there's no other R groups to stabilise a theoretical Carbocation (which would form if it was an Sn1 reaction (google it). So the only main alternative* is Sn2.
2.) Cyanide is well known as a nucleophilic or 'nucleus - loving' species.
.....due to it's large negative charge. Think of it as 'wanting' to spread out it's charge/electron density,
how can it do this? (Most solvents are inert)........ by attacking the electropositive (d+) CH3 center!
....The -CH3 center would be made slightly electropositive by the slightly more electronegative -Br group (d-), therefore the (d+) CH3 center 'wants' electron density, so we could call that an electrophile.
This is equally also a lewis acid base reaction as the Cyanide is acting as a Lewis base (electron donor) and the -CH3 center is acting as a lewis acid (Electron acceptor).....or you could also describe it using MO theory also!
So your products would be CH3-CN + Br- (with some sort of counterion like K+ from the Cyanide Salt in more realistic terms).
You can see chemistry doesn't rely on one model to explain things and you will find that there are many equivalent theories that each serve different purposes. The 'Nucleophilic' model I feel is better in this case as it describes the actual mechanism better and implies application of the Sn2 'rate label'. (Substitution Nucleophilic, 2nd order kinetics)...which can be used to derive the mechanism.
However with inorganic reactions and particularly reactions involving molecular formulae, it's typically better to use the Lewis or Bronsted Lowry theories when the exact reaction mechanism is not as important as e.g pH calculations or pKA, Lewis diagrams etc
*There is another one called SNi that occurs in special reactions involving sulfur.
I could complicate things more by talking about the different 'transition-states' and stereochemistry but that's a basic overview.