When it comes to understanding the details of something, there are a variety of synonyms for the phrase "the ins and outs". For example, you might refer to "the intricacies" or "the particulars" of a subject. Similarly, you could describe the nuances or subtleties that are involved in a situation. Understanding the "nuts and bolts" of something can also be a useful phrase to describe this kind of knowledge, as can "the finer points" or "the details". Depending on the context, you could also use "the complexities" or "the technicalities" as synonyms to convey a deeper level of understanding that requires attention to detail.