Your format is a bit ambigous, though I'm assuming since AM/PM isn't in there that the hours are in 24 hours format. Also not sure if the incoming date is day/month or month/day.
$date = new DateTime("3/6/2014 7:20");
echo $date->format('m/d/Y H:i');
Also not sure if the incoming date is day/month or month/day. But you can handle that with createFromFormat
$date = new DateTime::createFromFormat("n/j/Y G:i", "3/6/2014 7:20");
echo $date->format('m/d/Y H:i');
Read about date formats in the online docs. Also check out the DateTime book by the extension author to learn more.