You have to create a loop that goes over the value and dynamically generate the meta query. For example, assuming that your $_POST value is an array;
$meta_query = array('relation' => 'OR');
foreach ($_POST['year'] as $year) {
$meta_query[] = array(
'key' => 'year',
'value' => '".$year."',
'compare' => 'LIKE'
)
} // end foreach
$args = array(
'posts_per_page' => -1,
'meta_query' => $meta_query
);