my mac will not connect to the app store. why?

Should your Mac need newer than macOS 10.11.6 (an upgrade) or significant later system:

• How to get old versions of macOS - Apple Support

https://support.apple.com/en-us/HT211683

[Learn how to upgrade to macOS Big Sur, the latest version of macOS.]

• You can also use macOS Recovery to reinstall the macOS you're using now, upgrade

to the latest compatible macOS, or install the macOS that came with your Mac.

Another more technical way to upgrade a Mac (if needed) read/study these instructions:

• How to create a bootable installer for macOS - Apple Support

https://support.apple.com/en-us/HT201372

Did you try System Preferences > Software Update?

For details:

https://support.apple.com/en-us/HT201541