Should performance be not your highest goal, you can sort the keys of the hash by their values in descending order and pick the first one:

use warnings;
use strict;

my %hash=  ( '1', '8', '2', '6', '3','3' ,'4','7');
my @keys = sort { $hash{$b} <=> $hash{$a} } keys %hash;
print "Key with highest value is $keys[0].\n";
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