As mmcgeachy is suggesting, there are two parts to the answer to get the complete picture. One part is about the storefront platform itself (AspDotNetStorefront) and the second is in reguard to your hosting provider.
First, for the Storefront Itself neither, version 8.0.1,2 nor 9.2 of AspDotNetStorefront will support TLS 1.1 or TLS 1.2 as they are written on .NET library versions 2.0 and 3.5. Only AspDotNetStorefront versions 9.5 and 10 support TLS 1.1 and TLS 1.2. So, you will need to upgrade from your current version to get support for the more secure TLS protocol.
Web Hosting Provider
The second part is about your host provider's server. Does it support TLS 1.1 and TLS 1.2? You can ask them, or you can run a simple test by making a quick change to a setting in your browser. Follow the instructions in this link to learn how to setup IE, Chrome, and FireFox Then, go to your website and go into the shopping cart or any other secure page. If the page comes up, the host server supports TLS 1.2.
In Chrome, You can also click on the 'lock' in the broswer URL bar and review the connection details. It will tell you if the session is using TLS and which version.