You can also use GROUP BY twice.
DECLARE @push_number INT;
SET @push_number = [HERE_ADD_NUMBER];
WITH DistinctPrograms AS (
SELECT program_type, program_name
FROM cm_production
WHERE push_number = @push_number
GROUP BY program_type, program_name
)
SELECT program_type, COUNT(*) AS UniqueProgramCount
FROM DistinctPrograms
GROUP BY program_type;
This uses a CTE to pre-group distinct program names, then counts them.