In this program, you'll learn to add two matrices using multi-dimensional arrays in Java.

```
public class AddMatrices {
public static void main(String[] args) {
int rows = 2, columns = 3;
int[][] firstMatrix = { {2, 3, 4}, {5, 2, 3} };
int[][] secondMatrix = { {-4, 5, 3}, {5, 6, 3} };
// Adding Two matrices
int[][] sum = new int[rows][columns];
for(int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
sum[i][j] = firstMatrix[i][j] + secondMatrix[i][j];
}
}
// Displaying the result
System.out.println("Sum of two matrices is: ");
for(int[] row : sum) {
for (int column : row) {
System.out.print(column + " ");
}
System.out.println();
}
}
}
```

When you run the program, the output will be:

Sum of two matrices is: -2 8 7 10 8 6

In the above program, the two matrices are stored in 2d array, namely `firstMatrix` and `secondMatrix`. We've also defined the number of rows and columns and stored them in variables `rows` and `columns` respectively.

Then, we initialize a new array of the given rows and columns called `sum`. This matrix array stores the addition of the given matrices.

We loop through each index of both arrays to add and store the result.

Finally, we loop through each element in the sum array using a for (foreach variation) loop to print the elements.