uncomment the virtualhost directive and set as;
<VirtualHost *:80>
DocumentRoot "/var/www/html/rnd/public"
ServerName rnd.local
ServerAlias rnd.local
<Directory "/var/www/html/rnd/public/">
Options All
AllowOverride All
Order allow,deny
Allow from all
</Directory>
</VirtualHost>
restart apache
add an entry to your hosts file;
127.0.0.1 rnd.local
Check your routes.php and make sure that all your routes don't have any part of the server name in them, they are just plain as you would expect as routes within your site
revert your .htaccess file
<IfModule mod_rewrite.c>
<IfModule mod_negotiation.c>
Options -MultiViews
</IfModule>
RewriteEngine On
# Redirect Trailing Slashes...
RewriteRule ^(.*)/$ /$1 [L,R=301]
# Handle Front Controller...
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^ index.php [L]
</IfModule>
Visit rnd.local in your browser - hopefully it should be ok.
If you need another site, duplicate the virtualhost section changing the paths and the server name. Add new name in hosts.