Yes, I quite agree with BampaOwl. The verb "to know" in English has many different meanings. Of these, it can mean either "to have knowledge of something" or "to comprehend something." So out of context, "I don't know" and "I don't understand" sound like they mean the same thing. It is much easier in context, and the difference in meaning between the sentences "I don't have knowledge of why he went there" and "I am unable to make sense of why he went there" is easy to see. But without sufficient context, most people would have a hard time understanding the difference between "to know why" and "to understand why."
Maybe it is more important for us to think about correct usage of capire, comprendere, sapere and conoscere rather than English here. The most often phrase I both hear and use is Non ho capito, which is definitely "I have not understood." People often finish a sentence with the query " Capito?" I assume short for Hai Capito? or Ha capito?
But I don't understand! I don't understand how this all happens. How we go through this. I mean, I knew her, and then she's, there's just a body, and I don't understand why she just can't get back in it and not be dead anymore! It's stupid! It's mortal and stupid! And, and Xander's crying and not talking, and, and I was having fruit punch, and I thought, well she will never have any more fruit punch, ever, and she'll never have eggs, or yawn or brush her hair, not ever, and no one will explain to me why.
Conoscere carries the sense of "to be familiar with," "to be acquainted with," "to meet" or "to get to know"
Sapere is used with facts, data, specific pieces of information, names, phone numbers and addresses
e.g 'Conosco quella ragazza, ma non so il suo nome. - I know that girl, but I don't know her name'
Read the link below for further clarification
The key here is the "why." To many, many native speakers of English, "I don't know why" and "I don't understand why" mean essentially the same thing. So, yes, you can know something without understanding it. But you can not know why without understanding why. Not in English, that is.