use strict;
use warnings;
use 5.010; # only needed for say()

my @Array_1 = ("a1","a2","a3","a4","a5","a6");
my @Array_2 = ("a1","b2","c3","a4","f5","a6");
my @Array_3 = ("1","2","3","4","5","6");

my %seen;
@seen{@Array_2} = undef;
my @idx = grep exists $seen{$Array_1[$_]}, 0..$#Array_1;
@Array_1 = @Array_1[@idx];
@Array_3 = @Array_3[@idx];

say "@Array_1";
say "@Array_3";