Filtering post metas

Hi,
I Have several custom taxonomies (both hierarchical and non-hierarchical)
I want to filter out the custom taxonimies from the post-metas line, and display them on separate line, practically – the same as it’s displayed here: https://presscustomizr.com/snippet/show-random-posts-front-page/
or any other post there.

I need some guidance because the hooks API seem to be outdated.
TIA!