Can this lengthy if-else Java code be improved by using arrays?

As you stated, you could use arrays.

I would suggest 2 arrays

• One to hold the digits to catch
• Second one for the counts

Initialization of the arrays

char[] numbers = new char[10];

//initialize of numbers(char) to count
for(int i = 0; i < numbers.length; i++) {
  numbers[i] = (char) ('0' + i);
}

int[] counts = new int[10]; //no initialization needed because int is default 0

In the for-loop where you iterate over the line, add a nested for loop, that iterates over the numbers-array. Here is the whole while loop:

while (inFile.hasNextLine()) {
  String line = inFile.nextLine();
  for (int i = 0; i < line.length(); i++) {
    for(int j = 0; j < numbers.length; j++) {
      if(line.charAt(i) == numbers[j]) {
        counts[j]++;
      }
    }
  }
}

For the output just use another for over the arrays:

for(int i = 0; i < numbers.length; i++) {
  System.out.println("         "+ numbers[i] +"      " + counts[i]);
}

Edit: Another solution using a Map

//...

Map<Character, Integer> charCounts = new HashMap<>();

for (int i = 0; i < 10; i++) {
  charCounts.put((char) ('0' + i), 0);
}

while (inFile.hasNextLine()) {
  String line = inFile.nextLine();
  for (int i = 0; i < line.length(); i++) {
    charCounts.computeIfPresent(line.charAt(i), (key, val) -> val + 1);
  }
}

//...

for (Character number : charCounts.keySet()) {
  System.out.println("         " + number + "      " + charCounts.get(number));
}

With this solution you can easily extend your program to count any occuring character. Just remove the initialization of the map and add this line below the computeIfPresent.

charCounts.putIfAbsent(line.charAt(i), 1);

With Java 8 you can use Files.lines to get a Stream of all the lines in a file. Then you can transform the stream to a stream over every char using flatMap and in the end collect it to a map that has the Character as key and the count of the character as value.

try (Stream<String> stream = Files.lines(Paths.get(fileName)) {
    Map<Character, Long> charCountMap = stream
        .flatMap(line -> line.chars().mapToObj(c -> (char) c))
        .collect(Collectors.groupingBy(c -> c, Collectors.counting()));
    System.out.println("         0      " + charCountMap.getOrDefault('0', 0));
} catch (IOException e) {
    e.printStackTrace();
}

Probably the way I would do it in a real world scenario, because it's short, but just for practice the other answers are better.

Yes. I would say it can be simplified a great deal with an array. You don't need seperate sentinels for the values, you can check they are in range and then use Character.digit to parse them. Something like,

Scanner scan = new Scanner(System.in);
System.out.print("Enter name of the input file: ");
String fileName = scan.next();
try (Scanner inFile = new Scanner(new FileReader(fileName))) {
    int[] count = new int[10];
    while (inFile.hasNextLine()) {
        String line = inFile.nextLine();
        for (int i = 0; i < line.length(); i++) {
            if (line.charAt(i) >= '0' && line.charAt(i) <= '9') {
                count[Character.digit(line.charAt(i), 10)]++;
            }
        }
    }
    System.out.println("\n-= Count of Thistles in  =-");
    System.out.println("-= the Hundred Acre Wood =-\n");
    System.out.println("        -----------");
    System.out.println("        type  count");
    System.out.println("        -----------");
    for (int i = 0; i < count.length; i++) {
        System.out.printf("         %d      %d%n", i, count[i]);
    }
    System.out.println("        -----------");
}

You can use a single array for this and index notation. Each array index should hold the quantity of digits. Much more clear.

import java.io.FileReader;
import java.io.FileNotFoundException;
import java.util.Scanner;
    
public class Homework4A {

    public static void main(String[] args) throws FileNotFoundException {
        Scanner scan = new Scanner(System.in);
        System.out.print("Enter name of the input file: ");
        String fileName = scan.next();
        try (Scanner inFile = new Scanner(new FileReader(fileName))) {
            
            int[] count = new int[10];
            
            while (inFile.hasNextLine()) {
                String line = inFile.nextLine();
                for (int i = 0; i < line.length(); i++) {
                    try {
                        int c = Character.getNumericValue(line.charAt(i));
                        count[c] += 1;
                    } catch (Exception e) { }
                }
            }
            
            System.out.println("\n-= Count of Thistles in  =-");
            System.out.println("-= the Hundred Acre Wood =-\n");
            System.out.println("        -----------");
            System.out.println("        type  count");
            System.out.println("        -----------");
            for (int i = 0; i < 10; i++)
                System.out.println("         " + i + "      " + count[i]);
            System.out.println("        -----------");
        }
    }
}