The pairing is true if the difference between end of one string and start value of the other string is greater than 300.

Just turn your words into code :)

#!/usr/bin/perl
use strict;
use warnings;

my @data;
while (<DATA>) {
    push @data, [ $_, (split ' ')[2,3] ];  # [ input-line, start, end 
+]
}

my $cnt;
for my $d1 (@data) {
    for my $d2 (@data) {
        my $dist = $d1->[1] - $d2->[2];    # start of one - end of the
+ other
        if ($dist > 300) {
            print "Pair", ++$cnt, ":\n";
            print "      ", $d2->[0];
            print "      ", $d1->[0];
            print "Distance: $dist\n";
        }
    }
}

__DATA__
ACNGYNDHNG 10 1333 1343 1152
AVDVHVHNGG 10 209 219 2916
ACNGYNDHNGARRT 14 1333 1347 4608
GNDNNVNNRHNNNNVMNNVNNT 22 1589 1611 6291456
[download]

Output:

Pair1:
      AVDVHVHNGG 10 209 219 2916
      ACNGYNDHNG 10 1333 1343 1152
Distance: 1114
Pair2:
      AVDVHVHNGG 10 209 219 2916
      ACNGYNDHNGARRT 14 1333 1347 4608
Distance: 1114
Pair3:
      AVDVHVHNGG 10 209 219 2916
      GNDNNVNNRHNNNNVMNNVNNT 22 1589 1611 6291456
Distance: 1370
[download]

One approach would be to open the data file, then use a while loop to read it in and split (on whitespace) to obtain the values. Store those values in an AoA (see perllol). Once the data has been read in, close the datafile.

Next, use another while loop to shift a set of values from the AoA, then grep the remainder of the AoA with your distance calculation. Save and/or print results. The loop terminates once the AoA is empty.