If I weren't concerned about a comma appearing inside a quoted field, I might do this:

my $columns = 6; # or 10 or 14
local $/ = ',';
my @fields = ();
while (<>) {
    push @fields, $_;
    if ( scalar @fields == $columns ) {
        print @fields;
        @fields = ();
    }
}
print @fields;
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If I do think that a field might have a comma in it, I think I'd try to use Text::CSV.

use Text::CSV;

my $wholefile = do { local $/; <> };
my $parser = Text::CSV->new();
my $status = $parser->parse( $wholefile );
my @fields = $parser->fields();

my $columns = 6; # or 10 or 14
while ( @fields ) {
    my @line_fields = splice @fields, 0, $columns;
    my $csv = Text::CSV->new();
    my $status = $csv->combine( @line_fields );
    print $csv->string();
}
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I'm not really all that familiar with Text::CSV, so I wrote that based on the synopsis. Take it with a grain of salt.

Update: Since writing this, I notice that shmem saw something I missed, namely that the last column of the original file naturally does not have a comma between it and the first column of the original file. Neither of my solutions work in that case. The file would have to be repaired first, as suggested.