my $child_count = scalar @{ $barry{children} };
foreach my $child ( @{ $bary{children} ) {
    print $child->{name}, "\n";
    print $child->{age}, "\n";
    # etc.
}
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See perlreftut, perlref, and References quick reference.

just right, thanks

 code it is, sorry, and thanks

Next, please use warnings; use strict;, then clean up any errors and warnings.

That being said, I tried using perltidy to clean up your code the best I could, and I still got an error:

Can't call method "0" on unblessed reference
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How many children do you expect in your code? 1?

my $cnt = 0;
for (keys %barry) {$cnt++ if $_ eq 'children'}
print "cnt=$cnt\n";
__END__
cnt=1
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use strict;

my $barry = new Person ("Barry", 67);
$barry->AddKid(
    new Person("Jenny",38,"BA") ,
    new Person("Brendan",20,"student")
    );
print "---  $barry->{NAME} 's " .
   $barry->getKidCount . " children ---\n";
   
for my $kid(@{$barry->{CHILDREN}}){
    print $kid->{$_} ."\t" for qw[NAME AGE EDUCATION];
    print "-----------\n";
}

#-----------------------------

INIT{
package Person;
use strict;

sub new{
    my ($class,$name,$age,$edu) = @_;
    my $self= bless {
        NAME=>$name||"Anonymous",  AGE=>$age||0,
        CHILDREN =>[], EDUCATION=>$edu || "",
             }, $class;
    return $self;
}

sub AddKid{
    my $self = shift;
    push @ {$self->{CHILDREN} }, @_;

}

sub getKidCount{
    my $self = shift;
    return scalar @{$self->{CHILDREN}};
}
1
}
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my $num_children = @{ $barry{children} };
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print( scalar( @{ $barry{children} } ), "\n" );
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