This seems to be a question about finding all possible paths through a graph that end in "24". This does the job:

use strict;
use warnings;

use Graph::Directed;

my $g = "Graph::Directed"->new;

$g->add_edge(split ":") for qw(
    0:6
    0:12
    0:18
    0:24
    6:12
    6:18
    6:24
    12:18
    12:24
    18:24
);

# This doesn't protect against cyclic graphs
sub paths_from_vertex
{
    my $g = shift;
    my $v = shift;
    return unless $g->has_vertex($v);
    my @s = $g->successors($v);
    return [$v] unless @s;
    my @p = map { paths_from_vertex($g, $_) } @s;
    unshift @$_, $v for @p;
    return @p;
}

sub print_path
{
    my @path = @{+shift};
    for my $i ( 0 .. $#path-1 )
    {
        print "$path[$i]:$path[$i+1] ";
    }
    print "\n";
}

for my $i (0..24)
{
    print_path($_) for paths_from_vertex($g, $i);
}
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