Use WP_Query() to Output the 4th to 6th Most Recent Posts of a Custom Post Type

Yes, can achieve this with the offset parameter.

$homePageNews = new WP_Query( array(
    'posts_per_page' => 3,
    'offset'         => 3,
    'post_type'      => 'news'
) );

That will get 3 posts, but offset by 3, so that you get the 4th to 6th posts.

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