Theming/Aligning Multiple Views Blocks on Homepage
Please comment below if I have misunderstood anything and I can modify my answer.

First, I will clarify that I understand what is happening.

To the user, there appear to be 6 different pages on the site but in actuality, they are looking at the View Page that you posted above with contextual filters (each containing a different taxonomy term).

On the homepage, in a grid, you would like to display 6 Block Views that display the 4 most recent posts for their respective Taxonomy Term.

You would want Views to print out in a Bootstrap-like format so that they utilize the Bootstrap responsive grid.



This is what I recommend:


First we are going to create the first New Block.
Create a Block View called "Front Page News Blocks" (Or something along those lines) that lists Nodes of the Article type
Limit the View to only display 4 nodes
Ensure that it is sorted via post date (Ascending)
Add a "Custom text" field to the view and put the "More" link (with the btn and btn-primary classes) in the value
All of the above settings are "Applied to All Displays"
Now, you want to create some Block Views within this View. Have a total of 6 different Block Views
Within these, you can add categories Filters (but apply them only to the respective displays)
Also, override the URL in the "More" link in each view (Once again, don't forget to only apply it to the current display)
Create a template based on views-view.html.twig but name it after your View to override the default theme file
Within your custom TWIG file, you can add the "col-md-4" grid classes
You would also need to override the Homepage template so that you can add a div with the "row" class to the region where these blocks will be.
Now your CSS classes should be in the markup and you should be able to style your site as planned.

What I laid out was pretty generalized and high level. Definitely comment below if you need clarification on anything and I can edit this answer.

Hope this helps get you on the right track!