To solve this question, the user needs to understand the concept of object comparison in Java and how it differs from primitive type comparison.

In Java, objects are compared using the == operator. When comparing two objects using ==, Java checks if the two objects refer to the same memory location. If they do, the == operator returns true; otherwise, it returns false.

Now let's go through each option and explain why it is right or wrong:

A. Compiler error: This option is incorrect. There is no compilation error in the given code. The code will compile successfully.

B. Runtime Exception: This option is incorrect. There is no runtime exception in the given code. The code will run without throwing any exceptions.

C. True: This option is incorrect. Although the values of a and b are both 2, the variables a and b are objects of the Integer class. When comparing objects using ==, Java checks if they refer to the same memory location, not their values. In this case, a and b are different objects, even though their values are the same. Therefore, a == b will return false.

D. False: This option is correct. As explained earlier, a and b are different objects, even though their values are the same. Therefore, a == b will return false.

The answer is: D. False