When we speak of the phrase "dinning in to," we usually refer to having a particular idea or concept ingrained in our minds through repeated exposure or discussion. When trying to find synonyms for this phrase, we can consider terms such as "instilled in," "inculcated," "implanted," "imbued with," and "ingrained into," as they all convey the idea of something being deeply rooted or embedded in one's thinking. Other alternatives may include "enforced upon," "hammered home," "taught repeatedly," "cemented in," or "lodged in." All these terms convey the idea of a concept or notion becoming firmly anchored in one's mind.