Provide a flexible parser for LocalDate instances that can handle input in one of the following formats:
In this part of the code you already set a value for month and day
.parseDefaulting(ChronoField.MONTH_OF_YEAR, 1)
.parseDefaulting(ChronoField.DAY_OF_MONTH, 1)
Then you're trying to pass an input for month and year in your code
System.out.println(parser.parse("201411", LocalDate::from));
That you already set.