How to offset only a subselection of a set of nodes in a view
Here is one approach.

Make a view that lists all articles, no filter on "promoted to front page"

Now sort first by "promoted to front page", descending (so promoted articles come first), then by post date (or what ever else you want)

Now  limit it to 6 items.

Clone the view (or block display)

Change the limit setting so there is an offset of 6 (if you cloned the block display) make sure you save the new setting only for the new block (an override)