The easiest approach is to simply repeat the logic of the first while loop and create a second hash containing the words in the second text file. (It will help if you rename the first hash %results to something like %words1, then the second hash can be named %words2.) You now have only to find which keys are common to both hashes, and that will give you the desired result:

This is good advice; there's also List::Compare::Functional, which may make it easier to get the intersection of the two, e.g. (untested):

use feature qw/say/;
use List::Compare::Functional qw/get_intersection/;

# ...

my @common  = get_intersection( [keys %words1], [keys %words2] );
my $counter = scalar @common;

# output common words
say join "\n\n", @common;

# output count;
say "Found $counter words in common."
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EDIT: of course it's $counter, not $common; thanks Athanasius. (See what I meant about "untested"?)