How to use offset in WP_Query

offset is one of the arguments that you can pass to WP_Query, so it belongs in the $args array:

$args = array(
    'post_type'     => 'post',
    'category_name' => 'category',
    'orderby'       => 'date',
    'order'         => 'DESC',
    'showposts'     => 4,
    'offset'        => 4,
);

PS: $wp_query is a reserved variable used by the main query. When creating your own WP_Query instance you should use a different variable name.

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