If you want to do this from scratch: There’s two theme template files you can use for this:
searchform.php – this is rendered when you add a search widget to a sidebar. Add your dropdown boxes here.
search.php – this is where you’d write your custom Query using the submitted values from the form. The form submits via GET.
Check this out if you’re going to code yourself: https://codex.wordpress.org/Creating_a_Search_Page
However, you first might want to check out if a plugin would do what you want. I’ve never had use for anything like this, so I can’t speak to how well any plugins work for this type of application, but a quick search popped up with this: https://wordpress.org/plugins/ultimate-wp-query-search-filter/