Once you have reinstalled the appropriate drivers (whether through Multibeast or anything else), you can restart Mac OS X.
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For instance, if you're looking for the combo update to Mac OS X 10.8.4, simply search "10.8.4 combo update".
The official page from Apple tends to be the first search result.
* The Loan Product Advisor Feedback Certificate will include a feedback message to alert the Seller when these requirements must be met.
This installation process will take a few minutes-- once the installer finishes, it will ask you to reboot. You won't need to install the updates for 10.8.1, 10.8.2, or 10.8.3-- the combo update handles all of it for you.
A system update will probably overwrite a few of your Hackintosh's drivers.
However, this method is generally not recommended, as it doesn't give you a large measure of control over the updating process.
Instead, the preferred method of updating a Hackintosh is to install a "combo update".