List::Util is a core Perl module (ships with Perl) and provides a subroutine called first. That subroutine returns the actual element. But if you treat indexes as elements and reverse them you can get what you need:

#!/usr/bin/env perl

use strict;
use warnings;
use List::Util qw(first);

my @array = (1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,6);


my $idx = first {$array[$_] == 4} reverse 0..$#array;

print "$idx\n";
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If non-Core modules are allowed, which they ought to be, you can use List::MoreUtils, which provides lastidx, in which case you could do this:

#!/usr/bin/env perl

use strict;
use warnings;
use List::MoreUtils qw(lastidx);

my @array = (1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,6);


my $idx = lastidx {$_ == 4} @array;

print "$idx\n";
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If you don't want to use a module, just do this:

#!/usr/bin/env perl

use strict;
use warnings;

my @array = (1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,6);

my $idx;
for (reverse 0..$#array) {
    if ($array[$_] == 4) {
        $idx = $_;
        last;
    }
}

print "$idx\n";
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And then repent for not being willing to use a module (even though this is quite easy to solve without).