An approach very similar to stevieb's solution except:

• An array is used instead of a hash for button widget storage;
• The  i, j info is encapsulated in a callback and not stored in the widget array (and thus is not accessible other than through the ToggleBox() function - it's effectively immutable);
• Uses callbacks (see Tk::callbacks).

use strict;
use warnings;

use Tk;

my @frames;

my $mw = MainWindow->new( -bg=> '#606060', -borderwidth=> 0);
my $size = 40;
my $y = 0;
my $x = 0;
my $h = 3*$size;
for my $j (0 .. 15) {
    my $x = 0;
    my $w = 3*$size;
    for my $i (0 .. 15) {
        $frames[$i][$j] = $mw->Button( -text => ' ', -bg => "#60C8BC",
+ -fg => "#000000", -borderwidth => 1, -anchor => 'w',  );
        $frames[$i][$j]->bind('<Button-1>' => [ '::ToggleBox', $i, $j 
+] );  # bind to callback
        $frames[$i][$j]->place( -y=>$y, -x=>$x, -width=>$w, -height=>$
+h );
        $x = $x + $w;
        $w = $size;
        $x = $x+2 if ($i % 5 == 0);
    }
    $y = $y + $h;
    $h = $size;
    $y = $y+2 if ($j % 5 == 0);
}

MainLoop;

exit;

sub ToggleBox {
    my $self = shift;
    my ($jj, $ii) = @_;
    print "$jj, $ii\n";
    }
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