Display Posts includes many query parameters for determining which posts are shown. If you use the
category_id parameters and include multiple categories, it will find posts that have any of those categories.
If you would like to list only posts that have all of those categories, you can use the taxonomy query parameters.
[display-posts taxonomy="category" tax_term="blue, green" tax_operator="AND"]
Match all tags
The same applies to the “tag” taxonomy. If you use the
tag parameter and specify multiple tags, it will find posts with any of those tags.
Use a taxonomy query to get posts with all these tags:
[display-posts taxonomy="post_tag" tax_term="blue, green" tax_operator="AND"]