Well, if you're saving the database as a flat file, you'll want to chomp $borrower before you use it in an assignment, otherwise you're file will look like:

     Author's Name:Book/Borrower
     :Book:Book:Book 

rather than

     Author's Name:Book/Borrower:Book:Book:Book 

This would also explain why it looks like the author's other books seem to have been erased.

for my $author (keys %book) {
  print FILE $author;
  while (my ($book,$borrow) = each %{$book{$author}}) {
     print FILE ':' . $book;
     print FILE '/' . $borrow if $borrow;
  }
  print FILE "\n";
}
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Note: since this is homework I probably should not have given you that code, but well I did anyway....

I think what is meant is that the standard approach is to have your own "hand-coded" module of subroutines for your system, which, in particular, should have two subroutines, say getF and putF, which handle the writing to a file, for example:

sub getF
{
    # warning: untested "dreamware" ... I'll test later and
    # (if necessary) repost a correction

    # General routine to read any file into a hash 
    # (key-indexed) whose targets are anonymous hashes
    # (indexed by your column names)

    my ( $hashAdr,      # reference of hash to write back to - this on
+e
         $fileHandle,   # best not to hard-code these around the place
                        # but to have one subroutine per system
                        # that allocates unique ones, which would
                        # therefore get called in the main program
         $fileName,
         $fieldDelim,   # best use only one per PROJECT
                        # and if in doubt use "$;"
         $colNamArrAdr, # address of array of the column names -
                        # best to use all upper or all lower case
                        # if possible.
         $indexPosn     # can be e.g. "3" . $; . "4" to say
                        # that the index should be composed of columns
                        # 4 and 5 (surpri-ise!).
    ) = @_;

    %$hashAdr = ();     # initialise the hash

    while( <$fileHandle> )
    {
        chop;        # you know exactly one <CR> is there.
        my @cols = split( $fieldDelim, $_ );

        my $index = join( "", split( $;, $cols[ $indexPosn ] ) );
        # above is designed to handle 1 or more index columns

        foreach ( @$colNamArrAdr )
        {
           $$hashadr{ $index }{ $_ } = shift( @cols );
        }
    }
    return;
}
# the corresponding put routine is obvious from this, but
# I'll just mention the important loop:

foreach my $key ( sort( keys( %$hashAdr ) ) )
{
    my @output = ();

    foreach ( @$colNamArrAdr )
    {
        push( @output, $$hashAdr{ $key }{ $_ } );
    }

    print $fileHandle join( $fileDelim, @output ), "\n";
}
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