I know I am able to demote links I don't want to appear, but what I really want to do is reduce the number of site links from 6 to 4.
Does anyone know if this is possible or how to achieve it?
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Unfortunately there is no way currently to limit the number of site links you have on your Google search result entry. You can demote a site link URL from webmaster tools if you have added your web property to the search console.
Google automatically decides which URL's to set as site links, and while you can demote a URL from being a site link you can only demote up to 100 URL's, and only after they have been promoted to site links, and demotions are only effective for 90 days. Google also does not guarantee that URL's which have been demoted won't be promoted to a site link again in the future once the demotion expires.