It seems that you're on the right track. You just need to extract the left, right, top, and bottom coordinates from the corner points of each rectangle specification. This is easy to do using min and max from List::Util:

sub minmax { ( min(@_), max(@_) ) }  # helper function

for (@list_of_Num_Extraction) {
    if (/^(\d+),(\d+):(\d+),(\d+)$/) {
        my ($l,$r, $t,$b) = (minmax($1,$3), minmax($2,$4));
        for my $x ($l .. $r) {      # left to right
            for my $y ($t .. $b) {  # top to bottom
              $Unique_Num_List{($x-1)*$num_columns + $y} = "($x,$y)";
            }
        }
    }
    # and so on ...
}
[download]

Just to show that it works, here's a bit of code that uses the above method to draw rectangles onto a virtual screen (represented by a sparse array).

#!/usr/bin/perl -w

use strict;
use List::Util qw( min max );

sub minmax { ( min(@_), max(@_) ) }

# draw rectangles onto sparse screen matrix

my %screen;  # sparse screen matrix
my $rectangle_name = "A";
for (<DATA>) {
    if (/^(\d+),(\d+):(\d+),(\d+)$/) {
        my ($l,$r, $t,$b) = (minmax($1,$3), minmax($2,$4));
        for my $x ($l .. $r) {     # left to right
            for my $y ($t .. $b) { # top to bottom
                $screen{$y}{$x} = $rectangle_name;
            }
        }
    }
    $rectangle_name++;
}

# print out screen

for my $f (sub {$_/10 % 10}, sub {$_ % 10}, sub {"_"}) {
    print "   ", (map &$f, 1..20), "\n";
}

my ($ymin, $ymax) = minmax(keys %screen);

for my $y ($ymin .. $ymax) {
    printf "%2d|", $y;
    for my $x (1 .. 60) {
        print $screen{$y}{$x} || " ";
    }
    print "\n";
}

__DATA__
2,2:4,4
5,10:10,5
12,5:6,1
8,12:1,15
[download]

And the output:

   00000000011111111112
   12345678901234567890
   ____________________
 1|     CCCCCCC                                                
 2| AAA CCCCCCC                                                
 3| AAA CCCCCCC                                                
 4| AAA CCCCCCC                                                
 5|    BCCCCCCC                                                
 6|    BBBBBB                                                  
 7|    BBBBBB                                                  
 8|    BBBBBB                                                  
 9|    BBBBBB                                                  
10|    BBBBBB                                                  
11|                                                            
12|DDDDDDDD                                                    
13|DDDDDDDD                                                    
14|DDDDDDDD                                                    
15|DDDDDDDD
[download]

Cheers,
Tom

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