The subcategories that you see in the website snippet are the sitelinks, and Google decides which sitelinks should be added to the search results. The website owner cannot directly control it, but Google’s actions can be influenced to some extent. Here are some suggestions for you:
Clear Navigation: Ensure clear navigation for the website to ensure that consistency is maintained in forming categories and sub-categories in the website. This helps Google to better understand which pages are most critical and should be added as sitelinks.
Internal Linking: Follow consistency and hierarchy in internal linking to form a logical network. In this regard linking the homepage with other critical pages, like categories, about page, or contact us page, you can inform search engine crawlers which pages are most important on the website, and those can be added as sitelinks by Google.
Submit XML Sitemap: XML sitemap has the URLs of all the pages on the website; thus, submitting XML sitemap to Google Search Console helps the search engine crawlers to better understand the navigation/hierarchy of the website and the most critical pages on the website.
Schema Markup: Enabling schema markup helps search engine crawlers better understand the context of the website’s content, which improves the chances of critical pages becoming the sitelinks for the website.