Only show posts from a certain category?

You need to modify your WP_Query loop. Add a tax_query argument to filter the category you want.

$portfolioloop = new WP_Query(array(
    'paged'          => get_query_var('paged'),
    'post_type'      => 'news',
    'posts_per_page' => 4,
    'tax_query'      => array(
        // Note: tax_query expects an array of arrays!
        array(
            'taxonomy' => 'portfolio', // my guess
            'field'    => 'id',
            'terms'    => 51,
        ),
    ),
));

http://codex.wordpress.org/Class_Reference/WP_Query#Taxonomy_Parameters

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