From your question, it seems that you have the challenge in dealing with formatting, and then doing the subtraction. 
I would recommend Java Date and Time Apis for this purpose, using a formatter. 
A junit method to achieve your requirement is given below
@Test
public void testDateFormatUsingJava8() {
    CharSequence inputdateTxt = "6/5/18";
    DateTimeFormatter  formatter = DateTimeFormatter.ofPattern("M/d/yy");
    LocalDate inputDate = LocalDate.parse(inputdateTxt, formatter);
    System.out.println(inputDate.minusDays(2L).format(formatter));
}
@Test
public void testDateCalenderUsingStringSplit() {
    String inputdateTxt = "6/5/18";
    String[] dateComponenets = inputdateTxt.split("//");
    Calendar cal = Calendar.getInstance();
    //Know where are the year month and date are stored.
    cal.set(Integer.parseInt(dateComponenets[2]), Integer.parseInt(dateComponenets[0]), Integer.parseInt(dateComponenets[2]) );
    cal.add(Calendar.DATE,-2);
    DateFormat dateFormat = new SimpleDateFormat("M/d/yy");
    String pastDate = dateFormat.format(cal.getTime());
    System.out.println("Date is displayed as : "+ pastDate );
}
@Test
public void testDateCalenderUsingJavaUtilDateApi() throws ParseException {
    String inputdateTxt = "6/5/18";
    DateFormat dateFormat = new SimpleDateFormat("M/d/yy");
    Date date = dateFormat.parse(inputdateTxt);
    Calendar cal = Calendar.getInstance();
    cal.setTime(date);
    cal.add(Calendar.DATE,-2);
    String pastDate = dateFormat.format(cal.getTime());
    System.out.println("Date is displayed as : "+ pastDate );
The reason why I use "M/d/yy" is because your question does not pad the date and month fields in the input date with a zero. If there is a guarantee that you receive a padded value in the date and month field, using "MM/dd/yy" is suggested. 
See the following answer for your reference : 
DateTimeFormatterSupport for Single Digit Values
EDIT: considering the limitation to not use Java 8 Date Time APIs, I have added two other alternatives to solve the problem. The OP is free to choose any one of the solutions. Kept the Java 8 solution intact for information purposes.