Is this what you are looking for?
$query = new wp_query($arr);
$arr = array(
'author__in'=> array(2,4,6), //Authors's id's you like to include
'posts_per_page' => '12',
'paged' => $paged,
'tax_query' => array(
array(
'taxonomy' => 'category',
'field' => 'id',
'terms' => array ( $cat_ids ),
)
)
);