So my question is how to make that output look normal(like what it's supposed to be) ?

What ARE you expecting $h{word2} to contain, [[2,3],3] or [2,3,3] ?

Does this make you any wiser or perhaps you ought to check out the docs?

#!perl -w
use strict;

my %h = (
word1 =>[2,3],
word3 =>[1,2]
);
$h{word2} = [ $h{'word1'},3],
$h{word4} = [ @{ $h{'word1'} },3],

print $h{'word2'}->[0]->[0], "\n";       # Alternative1
print @{ @{ $h{'word2'} }[0] }[0], "\n"; # Alternative1

print @{ $h{'word4'}}[0], "\n";          # Alternative2
print $h{'word4'}->[0], "\n";            # Alternative2

__OUTPUT__
2
2
2
2
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