Try something like this, which includes the suggestions by davido and Anonymous_Monk. As CountZero has suggested, you may also need to check some or all of the index values as arrays start at element zero in Perl ... :-)

use strict; use warnings;

open my $bh, "<", $B_file or die "$0: open $B_file: $!";

my %bHash;

# slurp text file B
# could generate a unique key consisting of field 0 and 11, 
# but never mind.
foreach (<$bh>) {
   my @text=split(/\t/);
   $bHash{$text[0]} = $text[11];
} 

close $bh;

open my $ah, "<", $A_file or die "$0: open $A_file: $!";
# read in text file A
foreach (<$ah>) {
    my @text = split(/\t/);
    if ($bHash{$text[3]} eq $text[11]) {
       # we have a match, print it
       print join( "\t", @text[1..3]),"\n";
    }
}
close $ah;
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