Both anonymous and local inner classes can be defined inside a method, as Moojid demonstrated in his example.
In Java literature, we can say that enums are implicitly static. Because we can use it as Apple.bigApple, where Apple is an enum type. You know that static declarations (declarations of static variables/static classes) are not valid inside a method. Therefore we couldn't declare enums inside a method local. But this is a *one* reason only. There are some other technical reasons rely on that.