When should I appropriately use adjectives and adverbs?
This advice, taken literally, is absurd. Adjectives and adverbs are perfectly reasonable parts of speech, and there is no inherent reason to avoid them. If you pick up any piece of academic writing, it should be clear that nearly every sentence includes them, and could not reasonably be expressed without them.

I count four in your question itself: "academic", "another", "specific", "proper". I can't imagine how you would express your question without any.

It is generally good advice in academic writing to write concisely and avoid unnecessary words. And it is a little easier to add unnecessary adjectives and adverbs to a sentence than some other parts of speech, so they may deserve some extra scrutiny. But avoiding them altogether? Nonsense.