Use a module such as DateTime, Date::Manip, Date::Parse:

use strict;
use warnings;
use DateTime::Format::Strptime;

my $parser =
  DateTime::Format::Strptime->new( pattern => '%m/%d/%Y' );
while (<DATA>) {
    my $dt = $parser->parse_datetime( $_ );
    print $dt->ymd();
}

__DATA__
3/1/2006 0:00:00
7/22/2007 0:00:00
12/1/2006 0:00:00
12/22/2007 0:00:00
[download]

perl -l 628560.pl
2006-03-01
2007-07-22
2006-12-01
2007-12-22
[download]