i cant update my mac to big sur 11.6 it says my internet is to slow but my internet is working fine

Here is my two cents, for what it is worth. I am guessing that the reason you are unable to successfully install your operating system is because the installer became corrupted during the download. The reason for this is because these are very large files and if you are using Wi-Fi, it often is too slow for these large files. Put the installer into the trash and do another download. I suggest that you need to use an Ethernet cable directly connected to your modem/router. If necessary, temporarily move your computer to do the download. And during the process, stay off the internet. If you are unable to directly connect to the internet, then be prepared to do multiple Wi-Fi downloads until you get a good one that loads. And allow each download to fully complete, which can take up to an hour, more or less, plus another 45 minutes or so for the installation. Good luck. I hope it goes well.

But you have no control over the Internet within or beyond your ISP and there may be propagation delays between you and Apple servers that are triggering the 11.6 update to provide that message. Try again later.