- min: documentation ( source)
<?php
$date = new DateTime( '2016-08-25' );
echo $date->format('Y-m-d'),"\n";
$day = $date->format('j');
$date->modify('first day of sixth month');
$date->modify('+' . (min($day, $date->format('t')) - 1) . ' days');
echo $date->format('Y-m-d');