So a minor change to allow the closure to close on the current value would be to create new variables: 

#! /usr/bin/perl 
use warnings;
use strict;
use Tk;

my $mw = MainWindow->new;
$mw->title("Checkbutton Grid");

my $x_size = 5;
my $y_size = 5;
my %b_name;

for (my $x=0; $x<$x_size; ++$x) {
    for (my $y=0; $y<$y_size; ++$y) {
        my $x_cord = $x;
        my $y_cord = $y;
        $mw -> Checkbutton (
                            -activebackground => "white",
                            -command => sub { print "$x_cord,$y_cord\n
+";
                                print "hi"; }
                           ) -> 
            grid (
                  -row => $x,
                  -column => $y
                 );
    }
}

MainLoop;

[download]
I'm not saying this is more efficient or better than your other example below (probably is neither), just that it's closer to the OP tried to do while still working.

In reply to Re^3: Perl/Tk : Trouble with commands and Checkbuttons by Tanktalus
in thread Perl/Tk : Trouble with commands and Checkbuttons by Petras

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