попробуйте это в первом упражнении:
String[] array = {"Hi", "there", "yeah"};
Intent goIntent = new Intent(this, NewAppActivity.class);
/*
* put extra with "array" as a key and the String[] with your values as the value to pass
* */
goIntent.putExtra("array", array);
startActivity(goIntent);
и во втором занятии:
Bundle extras = getIntent().getExtras();
if (extras != null) {
String[] array = extras.getStringArray("array");
}