Let me a bit of clarity.
first there is no free version for the extension Best Offer. It is an extension sold in the marketplace, and developed by a third-party developer.
Next it appears Best offer does not have a version for any AbanteCart v 1.3.0 or higher. If you are using AbanteCart v 1.3.0 or higher you need to contact the developer there is support button in the Marketplace to do so, or look in your MarketPlace account on your orders and there will be a get help button. If you are using AbanteCart v 1.2.xxxx then the below link may assist you in installation.
Next here is a link on how to install a MarketPlace Extension.
https://forum.abantecart.com/index.php?action=post;topic=9514.0;last_msg=37519