TL;DR

You will no doubt get a lot more and better responses if you reduce the problem and information to the minimum required.

You should also try to think of a better title. "Urgent" - urgent for you, maybe, but not for anyone else. "Biological problem" - well, if you have a biological problem, I suggest that you go and visit your GP :-) Most of us aren't biologists. We don't particularly care that you work in biology, no more than we care that people work in finance or construction or broadcasting. We're interested in the data structures and algorithms.

Thankyou Sir, for your kind suggestions. I apologize for all these mistakes. I should not repeat it again.

I notice you're referencing a few undefined variables (@sample1 ...), if you add strict/warnings, they'll warn you about that and other things, and in the process cut your development time in half!

I'd like to help, but your problem description is too long and wordy for me :)

Please read How do I post a question effectively? and post short sample input, expected/wanted output, actual output, and explain how the actual output of your program doesn't match the expected/wanted output.

You might write something like this

#!/usr/bin/perl --
use strict;
use warnings;
use Data::Dumper;
#~ use LIMS::MT_Plate;
#~ use Microarray;
use autodie; # dies if open/close... fail

Main( @ARGV );
exit( 0 );


sub Main {
    if ( @_ == 3 ) {
        print BreakSomePlates(@_);
    } else {
        Demo();
        print Usage();
    }
} ## end sub Main


sub BreakSomePlates {
    my( $infile, $queryplate, $plateno, $query ) = @_;
    open my ($inFh),  '<', $infile; 
    while(my $line = <$inFh>){
        chomp $line;
        WalkThe( $line );
    }
#~     return "The sample $query placed in $queryplate is the location
+ $sample_name of Master Plate\n";
}

sub WalkThe { rand 666 }

sub Demo {
    my ( $Input, $WantedOutput )  = DemoData();
    my $Output = BreakSomePlates( $Input, qw' plate 1 b2 ');
    require Test::More;
    Test::More->import( qw' no_plan ' );
    Test::More::is( $Output , $$WantedOutput, ' BreakSomePlates works 
+as designed ' );
}

sub Usage {
    <<'__USAGE__';

NAME
    well_identifier.pl - extract well location ...

USAGE
    well_identifier.pl
    well_identifier.pl infile platename platenumber query
    well_identifier.pl infile Plate1/Plate2 b2
    ...

ARGUMENTS
    - infile 
        path to BAC's 384 tab delimited text file
    - Plate Number
        Plate1/Plate2,Plate3 or Plate4
    - Query 
        i.e. b2

__USAGE__

}


sub DemoData {

    my $Input = <<'__One__';
something
__One__


    my $ExpectedOutput = <<'__Two__';
blah blah
__Two__

    return \$Input, \$ExpectedOutput ;
}
__END__
not ok 1 -  BreakSomePlates works as designed
#   Failed test ' BreakSomePlates works as designed '
#   at pm.921846.pl line 40.
#          got: ''
#     expected: 'blah blah
# '

NAME
    well_identifier.pl - extract well location ...

USAGE
    well_identifier.pl
    well_identifier.pl infile platename platenumber query
    well_identifier.pl infile Plate1/Plate2 b2
    ...

ARGUMENTS
    - infile
        path to BAC's 384 tab delimited text file
    - Plate Number
        Plate1/Plate2,Plate3 or Plate4
    - Query
        i.e. b2

1..1
# Looks like you failed 1 test of 1.
[download]

Thanks sir for guiding me. You have suggested a better way to describe a problem particularly the Usage subrutine. Form on-words I"ll try to use this method in my scripts. I apologize for writing long problem. My efforts were only to make my problem understandable to IT expert and perl monks and that is why I have write details

Well, I'm trying also to understand the problem

Although this is not directly related with your question, it looks to me that is the same problem as to find an unique name to each seedling of each seed tray in a greenhouse, all cells must be different, so you have a matrix for each plate, and them you need a parent hash covering all matrixes.

You could have either a "parent" hash with samples=Keys and cells=values or either want a hash when plate cells will be keys and values = sample tags. I think the former is better cause you can't repeat a sample tag, but you can have four cells named B5 in different trays

So if I'm not wrong this is a problem related with

1- to assign tags according some rules to each key/element of a hash of hashes. Something like to identify the sample_BXC35 (key) with its hash value "i'm-the-cell-AF23-in-the-fourth-small-sized-plate"

2 - to print a tridimensional hash, a hash of hashes covering all your "seed-trays"

I suggest to read about tridimensional hashes and maybe also you will find useful to read about the Data::Dumper module

And now the samples,

maybe we could see easier graphically

Distribution of the first sample "x"

BIG plate 24x16 cells.

   A  B   C  D  E   ...  M   N  O   P
1 x1  .  x2  . x3   ... x7   .  x8  .    
2 ---------------------------------------- # row of separation
3 x9  .  x10 . x11  ... x15  .  x16 .
4 ----------------------------------------
5 x17 .  x18 .           ...etc
6 ----------------------------------------
...
24
[download]

Distribution of the second sample "y": first you fill the spaces between the first sample, ok

   A  B   C  D  E  F    ...   N  O   P
1  . y1  .  y2  . y3    ...  y7   .  y8      
2 ---------------------------------------- # row of separation
3  . 
4 ---------------------------------------- # row of separation
5  y9
24
[download]

and then, all seems too random and confusing to me, y9 should be in B2, but you say this is in A5. Can you explain better this? (Forget the complicated names, call the samples simply: first, second, third and fourth or w,x,y and z if you prefer)