I add new custom field to load my Books genres (taxonomy) in to my "writer" page (category).
look at my settings: http://awesomescreenshot.com/0df4qucud7
I need to show the checked genres on my writer page. Of coure if theres no checked genres the code shows nothing (IF tag).
How can I get the values?
ACF Plugin: https://wordpress.org/plugins/advanced-custom-fields/
You are getting the term ID's of the selected genres. With the ID you can get a field like so get_field('field_name', 'genre-cat'); In this situation the genre-cat can be replaced for the output of your field with the term IDs (you would have to do this for each term selected, so use the foreach statement).
See full documentation from ACF on how to get values from a taxonomy term: http://www.advancedcustomfields.com/resources/get-values-from-a-taxonomy-term/