"He hears the duck."
Translation:Hij hoort de eend.
There is no rule. You are right in that you simply need to remember which article goes with which word. It's similar to learning whether to use "le" or "la" in French. We do have a lovely, thorough explanation of articles in Dutch courtesy of Lavinae: https://www.duolingo.com/comment/3732938
If you change hoort to hort the pronunciation changes from a long-o to a short-o. In singular conjugations double vowels rarely change to a single vowel because of that.
Have a look at this website: http://www.heardutchhere.net/DutchPronunciation.html