What type of reaction is the generic equation a + bc → ac + b?

This is a single displacement reaction. Where a single element can displace an element in another compound and form a new compound.
In  the reaction given;
a + bc --> ac + b
bc is a compound, if a is more reactive than b, it can take the place of b and form a new compound ac.
Since only one displacement reaction is taking place its called a single displacement reaction.