How to detect the touch event outside the navigation drawer

You have to handle the touch position in dispatchTouchEvent() method. Check more about touch hierarchy here

@Override    
public boolean dispatchTouchEvent(MotionEvent event) {
    if (event.getAction() == MotionEvent.ACTION_UP) {
        if (mDrawerLayout.isDrawerOpen(mRightDrawerListView)) {

            View content = findViewById(R.id.right_drawer);
            int[] contentLocation = new int[2];
            content.getLocationOnScreen(contentLocation);
            Rect rect = new Rect(contentLocation[0],
                contentLocation[1],
                contentLocation[0] + content.getWidth(),
                contentLocation[1] + content.getHeight());

            View toolbarView = findViewById(R.id.toolbar);
            int[] toolbarLocation = new int[2];
            toolbarView.getLocationOnScreen(toolbarLocation);
            Rect toolbarViewRect = new Rect(toolbarLocation[0],
                toolbarLocation[1],
                toolbarLocation[0] + toolbarView.getWidth(),
                toolbarLocation[1] + toolbarView.getHeight());


            if (!(rect.contains((int) event.getX(), (int) event.getY())) && !toolbarViewRect.contains((int) event.getX(), (int) event.getY())) {
                isOutSideClicked = true;
            } else {
                isOutSideClicked = false;
            }

        } else {
            return super.dispatchTouchEvent(event);
        }
    } else if (event.getAction() == MotionEvent.ACTION_DOWN && isOutSideClicked) {
        isOutSideClicked = false;
        return super.dispatchTouchEvent(event);
    } else if (event.getAction() == MotionEvent.ACTION_MOVE && isOutSideClicked) {
        return super.dispatchTouchEvent(event);
    }

    if (isOutSideClicked) {
        //make http call/db request
        Toast.makeText(this, "Hello..", Toast.LENGTH_SHORT).show();
    }
    return super.dispatchTouchEvent(event);
}