Hi, welcome. Regarding your code:

#!/usr/bin/perl

#<--------------------------# Where are 'use strict;', 'use warnings;'
+?
open $fb, "myfilename.txt"; # What if the file is missing?

while ($line=<$fb>)         # What if you forgot you're using $line el
+sewhere? 
{
        #<------------------# Perl ignores whitespace but why be messy
+?
    chomp($line);
    if ($.=<>){             # `=` is not a comparison operator!
            print length "$line";
                # ^---------# ... and then a newline character?
            }               # Odd indentation makes it hard to tell wh
+at this matches.
    #<----------------------# Perl ignores whitespace but why be messy
+?
}
[download]

Here is a cleaned up version. I trust you to do the work of looking up the documentation for things you don't recognize, so that you learn why it's better to do it as I've shown. (But not the only way, of course!)

use strict; use warnings; use feature 'say';

# This section creates a temporary file for testing
my $file = "/tmp/$0.txt";
open TMP, '>', $file or die "Died: $!";
print TMP for (<DATA>);
close TMP;
#-------------------------------------------------#

print 'Which line would you like to measure? ';
chomp( my $wanted = <STDIN> );
die 'Died: wanted line number required' if not $wanted;

open my $FH, '<', $file or die "Died: $!";

while ( my $line = <$FH> ) {
    chomp $line;
    if ( $. == $wanted ) {
        say "The length of line $wanted ('$line') is " . length $line;
        last;
    }
    say "Reached end of file before line $wanted" if eof;
}

# remove the test file
unlink $file;

__DATA__
heaven
heavenly
heavenns
abc
heavenns
heavennly
[download]

Hope this helps!