[TL;DR] Just use a sub-query.
If you are trying to use concatenation then you need to ensure that you delimit the terms with a string that is never going to appear in the values otherwise you will find non-distinct terms grouped together.
For example: if you have a two numeric column then using COUNT(DISTINCT col1 || col2)
will group together 1||23
and 12||3
and count them as one group.
You could use COUNT(DISTINCT col1 || '-' || col2)
but if the columns are string values and you have 'ab-'||'-'||'c'
and 'ab'||'-'||'-c'
then, once again, they would be identical once concatenated.
The simplest method is to use a sub-query.
If you can't do that then you can combine columns via string-concatenation but you need to analyse the contents of the column and pick a delimiter that does not appear in your strings otherwise your results might be erroneous. Even better is to ensure that the delimiter character will never be in the sub-string with check constraints.
ALTER TABLE mytable ADD CONSTRAINT mytable__col1__chk CHECK (col1 NOT LIKE '%¬%');
ALTER TABLE mytable ADD CONSTRAINT mytable__col2__chk CHECK (col2 NOT LIKE '%¬%');
Then:
SELECT COUNT(DISTINCT col1 || '¬' || col2)
FROM mytable;