Here is source code of the Program to Demonstrate Checkable Menu Items in Android. The program is successfully compiled and run on a Windows system using Eclipse Ide. The program output is also shown below.
Main Activity

package com.example.usingcheckablemenuitems;

import android.app.Activity;
import android.os.Bundle;
import android.view.Menu;
import android.view.MenuItem;

public class MainActivity extends Activity {

@Override
protected void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.activity_main);
}

@Override
public boolean onCreateOptionsMenu(Menu menu) {
// Inflate the menu; this adds items to the action bar if it is present.
getMenuInflater().inflate(R.menu.main, menu);
return true;
}

/*
* When a checkable item is selected, the system calls your respective
* item-selected callback method (such as onOptionsItemSelected()). It is
* here that you must set the state of the checkbox, because a checkbox or
* radio button does not change its state automatically. You can query the
* current state of the item (as it was before the user selected it) with
* isChecked() and then set the checked state with setChecked()
*/
@Override
public boolean onOptionsItemSelected(MenuItem item) {
switch (item.getItemId()) {
case R.id.save:
case R.id.delete:
if (item.isChecked())
item.setChecked(false);
else
item.setChecked(true);
return true;
default:
return super.onOptionsItemSelected(item);
}
}
}

Menu

<?xml version="1.0" encoding="utf-8"?>
<menu xmlns:android="http://schemas.android.com/apk/res/android" >

<group android:checkableBehavior="single" >
<item
android:id="@+id/delete"
android:title="Delete"/>
<item
android:id="@+id/save"
android:title="Save"/>
</group>

</menu>