I know that the array declaration below is correct:
String[][] arrayNew={{"teresa","human","jennifer"},{"18","20"},{"nothing"}};
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You are just creating a 2D array (An array of String array).
On this particular case, you created a jagged array.
You could do the same for int array as well:
int[][] array = {{1,2,3}, {4,5}, {6}};
Multidimensional arrays are array of arrays:
String[] arrayA; //Array of Strings
String[][] arrayB; //Array of (Array of Strings)
String[][][] arrayC; //Array of (Array of (Array of Strings))
String[][][][] arrayD; //Array of (Array of (Array of (Array of Strings)))