Which way should I use while writing this method?
From the way you describe the problem, it is clear that there only needs to be one method. That method is supposed to: "... prompts the customer for the car type. ... Your method will return a valid car type".

What you have presented here, is the guts of some code which prompts the user for a character value, and then another method which converts the char to a String type.

From what I can tell (and filling in some blanks) your code looks functional, but I am not certain it satisfies the requirements (for just one method).

I would start with the 'specification' for the method, and use that as a template for the code. I will make the assumption (as you have) that the method should return the 'full' name of the car type (i.e. return "Economy" instead of 'E').

The good things in your code are the use of the do {...} while(...) block. You have a good loop there, with good conditional exit criteria.

You have not shown us what input is so I will assume it is a Scanner on System.in.

If we wrap the code you have there with a method that makes sense, it would be something like:

public String promptForCarType(Scanner input) {
    .....
    return carType;
}


That would be a method that prompts the user for a car type, and returns the user's selection.

The code inside that is what you have written above. There are a few things you should consider though:


You should probably get the full input from the user (not just the first character), and make sure the user only entered a single character (data validation).
Do you know what a 'switch' statement is? It would be really neat in here (and would remove the need to call the carType(char) method).
When you have java methods that return a value, there is often no need to 'store' the return value to the end of the method... you can just return when you have it....
when dealing with user input, you should try to leave them an 'exit strategy', like "enter Q to quit"
if you do an early-return mechanism, there is no need to do any conditions in the loop, you can just do while (true) {...}


One possible method for you may be something like:

public String promptForCarType(Scanner input) {
    System.out.println("(E) Economy  - 50 TL");
    System.out.println("(M) Midsize  - 70 TL");
    System.out.println("(F) Fullsize - 100 TL");
    // add in a Q option here ....
    // the Scanner may not have input....
    while (true) { // convert to while loop.
        System.out.println("Enter the car type (E/M/F) : ");
        if (!input.hasNext()) {
            throw SomeExceptionToSayTheresNoMoreInput(....);
        }
        String userinput = input.next();
        // check that input is just one character long.....
        char type = userinput.charAt(0);
        type = Character.toUpperCase(type);
        switch (type) {
            case 'E' : return "Economy";
            .....   // other cases
            case 'Q' : throw new UserWantsToQuitException(".....");
            default : // no need for a default, the loop will just go around again
        }
    }
}