You can use Concatenate values from related records by Allen Browne for this. Copy the function code from that web page and paste it into a new standard module. Save the module and give the module a name different from the function name; modConcatRelated would work.
Then I think you should be able to use the function in a query even though you're not proficient with VBA.
First notice I changed the field names in TableA to replace spaces with underscores. With that change, this query ...
SELECT
sub.Operating_System,
ConcatRelated("Machine_Name", "TableA",
"Operating_System = '" & sub.Operating_System & "'") AS Machines
FROM [SELECT DISTINCT Operating_System FROM TableA]. AS sub;
... produces this result set:
Operating_System Machines
Linux Server01, Server02
Solaris Server05
Windows Server03, Server04
If you can't rename the fields as I did, use a separate query to select the distinct operating systems.
SELECT DISTINCT TableA.[Operating System]
FROM TableA;
Save that as qryDistinctOperatingSystems, then use it in this version of the main query:
SELECT
sub.[Operating System],
ConcatRelated("[Machine Name]", "TableA",
"[Operating System] = '" & sub.[Operating System] & "'") AS Machines
FROM qryDistinctOperatingSystems AS sub;
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