You need a German grammar book or website.
There are two main types of adjective endings, strong and weak. The adjective endings with -en are in the group called 'weak,' because they come after another word that already shows gender, case, and number.
Please search for "German" + "weak adjective endings." Here are some examples.
* A determiner is any der-word (der/das/die, dieser, jener etc.), or any ein-word with an ending (eine, einen, einem, keine,
keines, meine, seine, ihre, unsere etc., BUT NOT ein, kein, mein, sein, ihr, unser, euer).
* If there is a determiner preceding the adjective, the adjective will end in -e or -en ("weak endings"), according to the following table ...https://resources.german.lsa.umich.edu/gramma...https://www.bbc.co.uk/bitesize/guides/z87vrdm...https://www.fluentu.com/blog/german/german-ad...http://www.npenn.org/Page/7055https://germanstories.vcu.edu/grmn_202/adject...http://www.lonweb.org/links/german/lang/004.htmhttps://www.apronus.com/learngerman/adj.htmhttp://www.acampitelli.com/learning_weak_adje...
adjectives preceded by definite articles or der-words take weak adjective endings ...
When an adjective comes between a definite article or der-word and the noun it modifies, it takes weak adjective endings (because the article already gives enough grammatical information to signal the noun's gender, case and number).https://www.coerll.utexas.edu/gg/gr/adj_01.html