Thanks Juanito for adding the .NET 6 SDK to the extensions repository.
Here is some basic example output.
tc@box:~$ tce-load -wi dotnet6-sdk
tc@box:~$ mkdir hello
tc@box:~$ cd hello
tc@box:~/hello$ dotnet new console
Welcome to .NET 6.0!
---------------------
SDK Version: 6.0.100
The template "Console App" was created successfully.
Processing post-creation actions...
Running 'dotnet restore' on /home/tc/hello/hello.csproj...
  Determining projects to restore...
  Restored /home/tc/hello/hello.csproj (in 80 ms).
Restore succeeded.
tc@box:~/hello$ dotnet run
Hello, World!
tc@box:~/hello$ dotnet --info
.NET SDK (reflecting any global.json):
 Version:   6.0.100
 Commit:    9e8b04bbff
Runtime Environment:
 OS Name:     tinycore
 OS Version:  12.0
 OS Platform: Linux
 RID:         linux-x64
 Base Path:   /tmp/tcloop/dotnet6-sdk/usr/local/share/dotnet6-sdk/sdk/6.0.100/
Host (useful for support):
  Version: 6.0.0
  Commit:  4822e3c3aa
.NET SDKs installed:
  6.0.100 [/tmp/tcloop/dotnet6-sdk/usr/local/share/dotnet6-sdk/sdk]
.NET runtimes installed:
  Microsoft.AspNetCore.App 6.0.0 [/tmp/tcloop/dotnet6-sdk/usr/local/share/dotnet6-sdk/shared/Microsoft.AspNetCore.App]
  Microsoft.NETCore.App 6.0.0 [/tmp/tcloop/dotnet6-sdk/usr/local/share/dotnet6-sdk/shared/Microsoft.NETCore.App]
To install additional .NET runtimes or SDKs:
  https://aka.ms/dotnet-download