Let's say foo.txt has numerous lines of identical text, like this.

some random text
Hello World
some other random text
Hello World
even more random text
Hello World

Using a while loop and the $. operator, we can append each line number to the file.

open(FH, "<", "foo.txt");

while (my $line = <FH>) {
  print "$. $line";
}

close FH;

This will identify that line 6 is the last line that contains Hello World.

1 some random text
2 Hello World
3 some other random text
4 Hello World
5 even more random text
6 Hello World

We can then use this markup to store the last line into a variable, most appropriate called $last_line;

open(FH, "<", "foo.txt");

while (my $line = <FH>) {
  if ($line =~ /Hello World/) {
    $last_line = "$. $line";
  }
}

close FH;

my @last_line = split/ /, $last_line;

print "Line $last_line[0] in foo.txt contains the last occurrence of $last_line[1]\n";

Running this script will produce the following output.

Line 6 in foo.txt contains the last occurrence of Hello World