"You need to put on your socks."
Because -nIS always comes before -moH. It's just a grammatical rule. We don't really teach it in this course, but maybe we'll add it in if we expand the course in the distant future. Each of the suffixes gets grouped into numbered categories and must always appear in numerical order. -nIS is a Type 2 suffix and -moH is a Type 4 suffix. This -nIS must always occur before -moH and can mean either "need to cause" or "cause to need". Context will usually make it clear which is intended.
For now, if you want to learn more about suffixes and their categories, please refer to The Klingon Dictionary by Dr. Marc Okrand.
can mean either "need to cause" or "cause to need".
Not really. This is misleading. -nIS and -moH don't really get applied to each other. -nIS says that the subject needs to do the verb; -moH says the subject causes the verb to happen. The only question is whether "the verb" is just "verb" or "verb + -moH." In every example I can think of, -nIS + -moH gets interpreted as the causer, who is the subject, doing the needing, not the doer of the action. vISay'nISmoH I need to wash it, I need to cause it to be clean. I do the needing, and I do the causing, because both apply to the subject. I can't think of any circumstances where a verb like that has been interpreted in the sense of I cause it to need to be clean. It's not an impossibility, but I'd have to see it.
It's a subtle point, but important. Except for -be' and -qu', suffixes don't modify other suffixes. If you think that way, you're going to confuse yourself.