Is it possible to only display posts that have multiple categories selected?

Trying to understand if it possible to display a post that has multiple categories selected for it it. Here is an example.

Trying to build a filtering system. Drop-down A(DD-A) has one set of categories and Drop-down B has a different set.

When selecting option 1 from DD-A it would show all post within that category. Same for DD-B. When selecting an option from each drop down I would like the loop to spit out only the posts that have been checked with both those categories.

Currently I can only get it to return a everything from the selected options added together vs. only the posts that have both categories selected.

Hopefully I am making sense. I am using Ajax to return all this back on the same page dynamically on the fly so that complicates things a bit but wanted to get an idea if it is even possible before I expand on the other issues I am having.

Any suggestions would be greatly appreciated. Thanks for the time as always.