Yes you can do that but there are few limitations which you should consider before Hosting your site. But first you have to make sure whether your Internet Service Provider (ISP) supports running website from your Local machine and if it supports then how much bandwidth is allowed per month.
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Secondly, You should know how to install and configure a server software on your Computer.
Your Computer have to be logged on All the time in order to keep your website up, Otherwise in case if you Switch Off or Reboot your Computer then your website will not be available for that time span. Your site will load slowly because home internet connections are not designed for serving web pages.