When using an eval STRING; statement, I find it very helpful to build the string separately so that it can be examined with the Perl debugger (see perldebug) or even with a simple print point.

Win8 Strawberry 5.30.3.1 (64)  Sat 09/26/2020 11:37:04
C:\@Work\Perl\monks
>perl
use strict;
use warnings;

my $kards;
my $bad = 'AKQJT98765432KKKK';
my $card = 'K';

my $e_string = "$kards = $bad =~ tr/$card//";
# print "e_string: >$e_string< \n";  # for debug

eval $e_string;
print "1: Num of '$card' in $bad is == $kards \n";

my $kings = $bad =~ tr/K//;
print "2: Num of '$card' in $bad is == $kings \n";

__END__
Use of uninitialized value $kards in concatenation (.) or string at - 
+line 8.
Use of uninitialized value $kards in concatenation (.) or string at - 
+line 12.
1: Num of 'K' in AKQJT98765432KKKK is ==
2: Num of 'K' in AKQJT98765432KKKK is == 5
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On another topic...

You seem to have been going over code examples as a self-teaching exercise. That's commendable, but it should be pointed out that in practice, there are arguably better ways of handling the "count the occurrences of an arbitrary set of characters in a string" problem. eval is expensive, and it's better to avoid the guillotine when a scalpel will do. A couple of examples (of, I'm sure, many).

Win8 Strawberry 5.30.3.1 (64)  Sat 09/26/2020 12:14:28
C:\@Work\Perl\monks
>perl
use strict;
use warnings;

my $n_found;
my $string = 'AKQJT98765432KKKK';
my $set = 'AQK';

# s/// probably fastest in practice.
my $destroy = $string;  # s/// alters its target
$n_found = $destroy =~ s{ [\Q$set\E] }{}xmsg;
print "s///:  Num of '$set' in '$string' == $n_found \n";

# m// probably a bit slower, use of =()= a bit tricky.
$n_found =()= $string =~ m{ [\Q$set\E] }xmsg;
print "m//:   Num of '$set' in '$string' == $n_found \n";

# tr/// is fastest, but needs expensive eval for arbitrary sets.
$n_found = $string =~ tr/KAQ//;
print "tr///: Num of 'KAQ' in '$string' == $n_found \n";

__END__
s///:  Num of 'AQK' in 'AKQJT98765432KKKK' == 7
m//:   Num of 'AQK' in 'AKQJT98765432KKKK' == 7
tr///: Num of 'KAQ' in 'AKQJT98765432KKKK' == 7
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