Try the following:

int[][] multi = new int[5][10];

... which is a short hand for something like this:

int[][] multi = new int[5][];
multi[0] = new int[10];
multi[1] = new int[10];
multi[2] = new int[10];
multi[3] = new int[10];
multi[4] = new int[10];

Note that every element will be initialized to the default value for int, 0, so the above are also equivalent to:

int[][] multi = new int[][] {
  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }
};

... or, more succinctly,

int[][] multi = {
  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }
};

Looks like this is what you want

    int columns = 2;
    int rows = 2;

    String[][] newArray = new String[columns][rows];
    newArray[0][0] = "France";
    newArray[0][1] = "Blue";

    newArray[1][0] = "Ireland";
    newArray[1][1] = "Green";

    for(int i = 0; i < rows; i++){
        for(int j = 0; j < columns; j++){
            System.out.println(newArray[i][j]);
        }
    }

Here I'll explain the code:

This declares the size of your new 2D array. In Java (and most programming languages), your first value starts at 0, so the size of this array is actually 2 rows by 2 columns

    int columns = 2;
    int rows = 2;

Here you are using the type String[][] to create a new 2D array with the size defined by [rows][columns].

    String[][] newArray = new String[columns][rows];

You assign the values by its placement within the array.

    newArray[0][0] = "France";
    newArray[0][1] = "Blue";

    newArray[1][0] = "Ireland";
    newArray[1][1] = "Green";

Looping through i would loop through the rows, and looping through j would loop through the columns. This code loops through all rows and columns and prints out the values in each index.

    for(int i = 0; i < rows; i++){
        for(int j = 0; j < columns; j++){
            System.out.println(newArray[i][j]);
        }
    }

Alternatively, assignment can be a one-liner:

    String[][] newArray = {{"France", "Blue"}, {"Ireland", "Green"}};

But I don't like this way, as when you start dealing with larger sets of data (like 10,000+ points of data with many columns), hardcoding it in like this can be rough.

I highly recommend you stick with using the for-loop for initialization of arrays with primitive values. My recommendation is stronger in the case of a multidimensional array.

However, here is the way:

int a = 4;               // Number of outer array elements
int b = 2;               // Number of inner array elements

int[][] board = IntStream
    .range(0, a)                                               // iterate 0..3
    .mapToObj(i -> IntStream.range(0, b)                       // for each iteratoe 0..1
                            .map(j -> 1 + (i + (a + 1) * j))   // calculate the value
                            .toArray())                        // compose the inner array
    .toArray(int[][]::new);                                    // compose the outer array

Note that the IntStream is able to create an array of primitives since it is a sequence of primitive int-valued elements. its method IntStream::toArray reutrns int[].

The composition of the outer array is a bit tricky since int[] is no longer a primitive value but an array itself. There is needed to use a method IntStream::mapToObj which maps int to an object - then the Stream<int[]> is returned and the method Stream::toArray(IntFunction<A[]> generator) converting to array with parameter has to be used since you cannot convert Object[] to int[][].

The parameter passed is simple. int[][]::new is nothing different than i -> new int[a][b].

You would use

List<List<String>> listOfLists = new ArrayList<List<String>>();

And then when you needed to add a new "row", you'd add the list:

listOfLists.add(new ArrayList<String>());

I've used this mostly when I wanted to hold references to several lists of Point in a GUI so I could draw multiple curves. It works well.

For example:

import java.awt.BasicStroke;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.Point;
import java.awt.RenderingHints;
import java.awt.Stroke;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;
import java.util.ArrayList;
import java.util.List;
import javax.swing.*;

@SuppressWarnings("serial")
public class DrawStuff extends JPanel {
   private static final int PREF_W = 400;
   private static final int PREF_H = PREF_W;
   private static final Color POINTS_COLOR = Color.red;
   private static final Color CURRENT_POINTS_COLOR = Color.blue;
   private static final Stroke STROKE = new BasicStroke(4f);
   private List<List<Point>> pointsList = new ArrayList<List<Point>>();
   private List<Point> currentPointList = null;

   public DrawStuff() {
      MyMouseAdapter myMouseAdapter = new MyMouseAdapter();
      addMouseListener(myMouseAdapter);
      addMouseMotionListener(myMouseAdapter);
   }

   @Override
   public Dimension getPreferredSize() {
      return new Dimension(PREF_W, PREF_H);
   }

   @Override
   protected void paintComponent(Graphics g) {
      super.paintComponent(g);
      Graphics2D g2 = (Graphics2D) g;
      g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING, 
            RenderingHints.VALUE_ANTIALIAS_ON);
      g2.setStroke(STROKE);
      g.setColor(POINTS_COLOR);
      for (List<Point> pointList : pointsList) {
         if (pointList.size() > 1) {
            Point p1 = pointList.get(0);
            for (int i = 1; i < pointList.size(); i++) {
               Point p2 = pointList.get(i);
               int x1 = p1.x;
               int y1 = p1.y;
               int x2 = p2.x;
               int y2 = p2.y;
               g.drawLine(x1, y1, x2, y2);
               p1 = p2;
            }
         }
      }
      g.setColor(CURRENT_POINTS_COLOR);
      if (currentPointList != null && currentPointList.size() > 1) {
         Point p1 = currentPointList.get(0);
         for (int i = 1; i < currentPointList.size(); i++) {
            Point p2 = currentPointList.get(i);
            int x1 = p1.x;
            int y1 = p1.y;
            int x2 = p2.x;
            int y2 = p2.y;
            g.drawLine(x1, y1, x2, y2);
            p1 = p2;
         }
      }
   }

   private class MyMouseAdapter extends MouseAdapter {
      @Override
      public void mousePressed(MouseEvent mEvt) {
         currentPointList = new ArrayList<Point>();
         currentPointList.add(mEvt.getPoint());
         repaint();
      }

      @Override
      public void mouseDragged(MouseEvent mEvt) {
         currentPointList.add(mEvt.getPoint());
         repaint();
      }

      @Override
      public void mouseReleased(MouseEvent mEvt) {
         currentPointList.add(mEvt.getPoint());
         pointsList.add(currentPointList);
         currentPointList = null;
         repaint();
      }
   }

   private static void createAndShowGui() {
      JFrame frame = new JFrame("DrawStuff");
      frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
      frame.getContentPane().add(new DrawStuff());
      frame.pack();
      frame.setLocationRelativeTo(null);
      frame.setVisible(true);
   }

   public static void main(String[] args) {
      SwingUtilities.invokeLater(new Runnable() {
         public void run() {
            createAndShowGui();
         }
      });
   }
}