Yes we must use equals method.
When a user inputs the abbreviation the String is constructed with the new operator and hence new String object is created. This "==" checks if both the references are pointing to the same object. For example in this case if user inputs the abbreviation as M, then a String M is created using new operator. Now when we compare --> if (day == "M"). Now this second "M" is actually another object which resides in string pool constant. As the objects are different the "if " would result in false and hence would not work. So use "equals" method