Your original code as BrowserUK said is writing the replacement after moving past the 2. And moritz is right that reading from the file and writing to a temp is better most of the time. If you have forgo the the temp file, something like the following could work:

open FH, '+<afile';
$temp = '';
  while (<FH>) {
  s/2/two\nhi hello/;
  $temp .= $_;
}
seek(FH, 0, 0);
print FH $temp;
truncate(FH, tell(FH));
close(FH);
[download]

this deals with the '2' when it finds it instead of after passing it. As long as your file isn't huge, like a logfile, this isn't too much of a memory hog. If I'm going to do it in memory, I do something more like the following than all that "IOish" stuff above.

sub slurp {
    my  $file = shift;
    open my $fh, '<', $file or return undef;
    local $/ unless wantarray;
    return <$fh> if defined wantarray;
}
sub jot {
    my $notepad = shift;
    open my $fh, ">", $notepad or die $!;
    print $fh @_;
}
my $temp = slurp 'file.txt';
$temp =~ s/2/two\nhi hello/;
jot 'file.txt', $temp;
[download]

The lexically scoped filehandle, $fh, goes out of scope when slurp returns and $fh is automatically closed before jot begins. slurp will return an array of lines if called with an array, or a string containing the whole file if called with a scalar as I did.