my @array = qw/ foo bar baz quux /;
my %hash  = qw/ f1  baz f2  foo  /;
my @newarray;

foreach my $thing (@array)   {
   push @newarray, $thing
     if grep { $_ eq $thing } values %hash;
}

print "newarray - @newarray\n";

__output__

newarray - foo baz