Displaying direct children of other pages on homepage

 $the_query = new WP_Query( array( 'post_type' => 'page', 'parent' => 42, 'child_of' => 0,) );

You should edit this line like following:

$the_query = new WP_Query( array( 'post_type' => 'page', 'post_parent' => 42) );

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