#!/usr/bin/perl
use strict;
use Tie::File;
use List::Util qw/shuffle/;
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You should also include the warnings pragma (it would have warned you about one of the lines of your program.)

#!/usr/bin/perl
use warnings;
use strict;
use Tie::File;
use List::Util qw/shuffle/;
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my $line;
my $i=0;
my @array;
my $count=0;
my $alphaFile = 'alphabetFile.txt';
my $numberFile = 'numberFile.txt';
my $fileCounter = 'counter.txt';
my $tempFile = 'temp.txt';

open(FILECOUNTER,$fileCounter);
$count = <FILECOUNTER>;
chomp($count);
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Why are these lines in file scope?    They should be inside the subroutine.    You should also verify that open worked correctly.

&readfile();
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There is no need to prepend an ampersand when using subroutine calls and it may cause unwanted side effects.

    tie @array, 'Tie::File', $numberFile || die("failed to open $numbe
+rFile");;
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You should declare @array here where you first use it instead of at file scope.

You are using the high precedence || operator which means that you are testing the boolean value of $numberFile NOT the success or failure of tie.

    tie my @array, 'Tie::File', $numberFile or die "failed to open $nu
+mberFile";
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    if (-e $tempFile) {
        open(TEMPFILE,"+<$tempFile") || die("failed to open $tempFile"
+);
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There is no need to stat the file first, just let open do its job:

    if ( open TEMPFILE, '+<', $tempFile ) {
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    my $counter=0;
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You never use this variable anywhere??

    tell(TEMPFILE);
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You are using tell in void context so this line is superfluous.    (The warnings pragma would have warned you of this.)

    while ($line = <CHARFILE>) {
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You should declare $line here where you first use it instead of at file scope:

    while ( my $line = <CHARFILE> ) {
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            if ("$line $array[$i]") {
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This test is superfluous because the string "$line $array[$i]" is ALWAYS true.

                foreach ( $line ) {
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You are looping over a list with one element.    The foreach loop aliases $line to $_ but you are not using $_ inside the loop so it is superfluous.

                        print shuffle $array[$i] . "\n";
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shuffle works on a list and returns a shuffled list but you are only passing shuffle a single element, the string "$array[$i]\n", so there is nothing really for shuffle to do, except return that one element.

                        print "\n" . $line . " " . rand "$array[$i]" .
+ "\n";
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You have three problems there: 1) rand works with numbers but you are copying the contents of $array[$i] to a string, so perl has to convert that string to a number for rand to work, and: 2) because of the high precedence of the concatenation operator you are actually passing rand the string "$array[$i]\n" which means that: 3) the newline is not printed out as you may have expected.

That will work correctly if you use the comma operator instead:

                        print "\n", $line, " ", rand $array[ $i ], "\n
+";
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You should also include the $! in your error messages when using open so you know why it failed.