This week's book giveaway is in the OCPJP forum. We're giving away four copies of OCA/OCP Java SE 7 Programmer I & II Study Guide and have Kathy Sierra & Bert Bates on-line! See this thread for details.
if create a object which has instance variable, inside a method then it will exist in heap memory or stack?
You need to understand the difference between an object and a reference to an object. An object is always on the heap (there is an exception, but let's not get into that ... ). A reference, can be on the heap, if it is part of the object, such as an instance variable. Or it can be on the stack, when it is declared locally, such as a local variable or a parameter.
Now as for your question...
There is no such thing as an instance variable inside a method. Variables declared inside a method are local variables.
local object state is not distributed by other threads because object reference variable is local ? or local object state is distributed by other threads because object is in heap ?
Again, you need to understand the difference between an object and a reference to an object.
Each method will have a local variable which will have there own copy of the reference. This reference will point to an object on the heap. Now... this reference can point to a privat copy of the object -- if it is instantiated in the method. Or it can point to a object, that all objects refer to.
Just because an object is on the heap, doesn't mean that it is shared. It depends on how you coded your application.