It will take some time for many South Koreans to ___________ the conflicting images of North Korea, let alone to___________ what to make of their northern cousins.

The key word in the given statement is let alone. It is synonymous with never mind, which is used to indicate that something is far less likely than the one already mentioned. For example, He cannot even run a kilometre, let alone participate in a marathon. So, the thing which is mentioned before this let alone phrase has to be of a lesser degree or extent.
Option (a) is correct, because reconcile means solving a matter, or restoring friendly relations (North and South Korea separated after World War II), so it will take them time to conclude what really went wrong with North Korea.
Option (b) is wrong, because understanding just means to comprehend or get it and clarify means to make things clear but does not refer to coming to a conclusion. Option (c) is wrong because make out can mean detect with senses. Option (d) is wrong because, understand is different from deciding.