Consider this solution:

#!/usr/bin/perl -w 
######################################################################
+##
use strict;
use Tie::File;

tie my @fin,"Tie::File","multilines.txt" or die $!;


for(my $ix=0;$ix <= $#fin;$ix+=4){
    my @lines=();
    foreach (my $iy=0;($iy < 4) && (($ix+$iy)<=$#fin);$iy++){
        push @lines, $fin[$ix+$iy];
    }
    printf "Lines starting with line %d:\n%s\n\n",$ix+1,join("\n",@lin
+es);
}

untie @fin;
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Tie::File lets you play with files as if they were arrays and is part of the standard Perl distribution.