#!/usr/bin/perl

use strict;
use warnings;

my $cur = -10;
my $x = qr'Begin';
my $y = 3;

while (<DATA>) {
  $cur = $. if /$x/;
  print if ($.>$cur and $.<=$cur+$y);
}

_ _DATA_ _
Hello
Welt Begin Test
ALPHA
BETA
GAMMA
DELTA