（ネストされたスクロールビューで）ビューページャーにフラグメントを追加しているときに、デバイスの戻るボタンでアプリケーションを終了できません

ViewPagerにサードパーティのライブラリを使用しているため、問題が発生していると思います。「activity_main.xml」ファイルの代わりに、次のコードをコピーして貼り付けるだけです。

<?xml version="1.0" encoding="utf-8"?>
<android.support.v4.widget.DrawerLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:id="@+id/drawer_layout"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:fitsSystemWindows="true"
tools:openDrawer="start">

<android.support.design.widget.CoordinatorLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    tools:context=".Main2Activity">

    <android.support.design.widget.AppBarLayout
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:theme="@style/AppTheme.AppBarOverlay">

        <android.support.v7.widget.Toolbar
            android:id="@+id/toolbar"
            android:layout_width="match_parent"
            android:layout_height="?attr/actionBarSize"
            android:background="?attr/colorPrimary"
            app:popupTheme="@style/AppTheme.PopupOverlay" />
        <android.support.design.widget.TabLayout
            android:id="@+id/tabs"
            android:layout_width="match_parent"
            android:layout_height="wrap_content" />
    </android.support.design.widget.AppBarLayout>

    <include layout="@layout/content_main2" />

    <android.support.design.widget.FloatingActionButton
        android:id="@+id/fab"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_gravity="bottom|end"
        android:layout_margin="@dimen/fab_margin"
        app:srcCompat="@android:drawable/ic_dialog_email" />

</android.support.design.widget.CoordinatorLayout>

<android.support.design.widget.NavigationView
    android:id="@+id/nav_view"
    android:layout_width="wrap_content"
    android:layout_height="match_parent"
    android:layout_gravity="start"
    android:fitsSystemWindows="true"
    app:headerLayout="@layout/drawer_header"
    app:menu="@menu/menu_drawer" />

</android.support.v4.widget.DrawerLayout>

このようにフラグメントをViewPagerに初期化しました

ViewPager viewPager2 = findViewById(R.id.viewpager);
    MyFragmentPagerAdapter pagerAdapter2 = new MyFragmentPagerAdapter(getSupportFragmentManager());
    pagerAdapter2.addFragment(TestFragment.createInstance(),"Home");
    viewPager2.setAdapter(pagerAdapter2);
    TabLayout tabLayout2 = findViewById(R.id.tabs);
    tabLayout2.setupWithViewPager(viewPager2);

これがTestfragment.javaクラスです

public class TestFragment extends Fragment {

public static TestFragment createInstance() {
    TestFragment profileFragment = new TestFragment();
    return profileFragment;
}

@Nullable
@Override
public View onCreateView(LayoutInflater inflater, @Nullable ViewGroup container, @Nullable Bundle savedInstanceState) {
    View rootView = inflater.inflate(R.layout.fragment_jadvalyab, container, false);
    return rootView;
}

@Override
public void onViewCreated(View view, @Nullable Bundle savedInstanceState) {
    super.onViewCreated(view, savedInstanceState);
}

@Override
public void onAttach(Context context) {
    super.onAttach(context);
}
}

そして、「Main2Activity.java」クラスの完全なコードはここにあります

public class Main2Activity extends AppCompatActivity
    implements NavigationView.OnNavigationItemSelectedListener {

@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_main);
    Toolbar toolbar = (Toolbar) findViewById(R.id.toolbar);

    FloatingActionButton fab = (FloatingActionButton) findViewById(R.id.fab);
    fab.setOnClickListener(new View.OnClickListener() {
        @Override
        public void onClick(View view) {
            Snackbar.make(view, "Replace with your own action", Snackbar.LENGTH_LONG)
                    .setAction("Action", null).show();
        }
    });

    DrawerLayout drawer = (DrawerLayout) findViewById(R.id.drawer_layout);
    ActionBarDrawerToggle toggle = new ActionBarDrawerToggle(
            this, drawer, toolbar, R.string.navigation_drawer_open, R.string.navigation_drawer_close);
    drawer.addDrawerListener(toggle);
    toggle.syncState();

    NavigationView navigationView = (NavigationView) findViewById(R.id.nav_view);
    navigationView.setNavigationItemSelectedListener(this);
    initViewPager();
}

private void initViewPager() {
    ViewPager viewPager2 = findViewById(R.id.viewpager);
    MyFragmentPagerAdapter pagerAdapter2 = new MyFragmentPagerAdapter(getSupportFragmentManager());
    pagerAdapter2.addFragment(TestFragment.createInstance(),"Home");
    viewPager2.setAdapter(pagerAdapter2);
    TabLayout tabLayout2 = findViewById(R.id.tabs);
    tabLayout2.setupWithViewPager(viewPager2);
}

@Override
public void onBackPressed() {
    DrawerLayout drawer = (DrawerLayout) findViewById(R.id.drawer_layout);
    if (drawer.isDrawerOpen(GravityCompat.START)) {
        drawer.closeDrawer(GravityCompat.START);
    } else {
        super.onBackPressed();
    }
}

@Override
public boolean onCreateOptionsMenu(Menu menu) {
    // Inflate the menu; this adds items to the action bar if it is present.
    getMenuInflater().inflate(R.menu.main2, menu);
    return true;
}

@Override
public boolean onOptionsItemSelected(MenuItem item) {
    // Handle action bar item clicks here. The action bar will
    // automatically handle clicks on the Home/Up button, so long
    // as you specify a parent activity in AndroidManifest.xml.
    int id = item.getItemId();

    //noinspection SimplifiableIfStatement
    if (id == R.id.action_settings) {
        return true;
    }

    return super.onOptionsItemSelected(item);
}

@SuppressWarnings("StatementWithEmptyBody")
@Override
public boolean onNavigationItemSelected(MenuItem item) {
    // Handle navigation view item clicks here.
    int id = item.getItemId();

    if (id == R.id.nav_camera) {
        // Handle the camera action
    } else if (id == R.id.nav_gallery) {

    } else if (id == R.id.nav_slideshow) {

    } else if (id == R.id.nav_manage) {

    } else if (id == R.id.nav_share) {

    } else if (id == R.id.nav_send) {

    }

    DrawerLayout drawer = (DrawerLayout) findViewById(R.id.drawer_layout);
    drawer.closeDrawer(GravityCompat.START);
    return true;
}
}

編集：

「content_main2.xml」のコード

<?xml version="1.0" encoding="utf-8"?>
<android.support.v4.widget.NestedScrollView xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:fillViewport="true"
app:layout_behavior="@string/appbar_scrolling_view_behavior">

<android.support.v4.view.ViewPager
    android:id="@+id/viewpager"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    app:layout_behavior="@string/appbar_scrolling_view_behavior" />

</android.support.v4.widget.NestedScrollView>

「fragment_jadvalyab.xml」のコードは次のとおりです

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout
xmlns:android="http://schemas.android.com/apk/res/android" android:layout_width="match_parent"
android:layout_height="match_parent">
<TextView
android:layout_width="match_parent"
android:layout_height="match_parent"
android:text="Best Wishes"
android:gravity="center"/>
</LinearLayout>