Not a 'smart' way.. but here goes:

use strict;

my @a=qw(a b c d);
my @b=qw(b a e f);

# this does exactly what your pair of 'for' loops 
# did...
my @m = map {
    my $x = $_;
    grep { /^$x$/ } @b;      
} @a;
 
print @m;
print "\n";
[download]

Prints output:

ab
[download]

UPDATE 1: A slightly 'smarter' alternative here ;)

use strict;

my @a=qw(a b c d);
my @b=qw(b a e f);

my %h;
my @m = map {$h{$_}++ ? $_ : ()} (@a, @b);
 
print @m;
print "\n";
[download]

This time, I'm using a hash to keep count of number of tiems a value is found in both arrays. For any value that's been counted more than once, I dump it into the @m array.

_____________________

$"=q;grep;;$,=q"grep";for(`find . -name ".saves*~"`){s;$/;;;/(.*-(\d+)
+-.*)$/;
$_=["ps -e -o pid | "," $2 | "," -v "," "];`@$_`?{print"+ $1"}:{print"
+- $1"}&&`rm $1`;
print$\;}
[download]