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use Modern::Perl;

...
say $fh "Position of $positions{$_} ends at $_"
  for sort { $a <=> $b } keys %positions;
close $fh;

Position of A ends at 2
Position of T ends at 3
...
Position of T ends at 9
Position of A ends at 13
Position of T ends at 14

use Modern::Perl;
use Sort::Naturally;
...
open my $fh, '>', 'Results.txt' or die $!;
say $fh "$_ ends at $positions{$_}" for nsort keys %positions;
close $fh;

A=1 ends at 2
A=2 ends at 5
...
T=2 ends at 6
T=3 ends at 9
T=4 ends at 14