This can be tricky, but it's important to note the differences have very little to do with the differences between"up" and "down" as words on their own. Describing a clear pattern is difficult, as both deal with the notion of "separate". Here are some example uses. Relationships break up: two people end a romantic relationship, companies end an alliance, countries stop working together. You also end fights by "breaking them up." Break up can also mean to "break into pieces." "I broke up that candy bar." Things "break down" when they stop working. "My car broke down on the way to work." "My body is slowly breaking down as I get older." Analyzing a situation in depth: "Let's break down the costs for this item."

These two mean basically the same thing and are often interchangeable. I believe these are called phrasal verbs. However, "break down" is often used to describe machines which stop working. You would not use "break up" for this. It is also used when details about the parts are required. For example, if a person gives you a bill you could ask for a "break down" of the bill, meaning you want details about each item which was charged. "Break up" is often used to describe people in a relationship who stop being in a relationship. You would not say "break down" for this. In addition to these there are the nouns "breakdown" and "breakup". Part of the reason for the above exceptions is these words. "Breakdown" specifically means a failure of a system, especially a machine. "Breakup" specifically means physical disintegration, or ending a relationship. As an example, "The breakup of my brother and his girlfriend caused my girlfriend and I to break up." "The car broke down. The breakdown was caused by poor maintenance." "Children, please break down into groups. After you break up into groups, follow the instructions on the chalkboard."

The simple answer, Judy, is that you can't - not without context. When it comes to phrasal verbs, context is vital. In some cases these two phrasal verbs can have almost the same meaning, and in others they can have totally different meanings. Business English Ed has given you some very good examples of how each of them is used, but remember - unless they're in a sentence, they mean nothing at all.