It just goes to show you how they really are perfect predators.
That is a sentence that you want your students to be able to understand and produce.
"How" is an adverb. "What" is an adjective.* Those words have different relationships to the clauses which contain them.
Let's start with a simple independent clause in canonical word order:
they really are perfect predators
Adjectives modify nouns and noun phrases. We could modify "perfect predators" with an adjective like "such":
they really are such perfect predators
More relevantly, we could almost modify that phrase with an adjective like "what":
*they really are what perfect predators
The "what" isn't happy with being stuck in the middle of the clause. This is especially true if we're going to use it to make the clause subordinate. We need to move the entire phrase containing "what" to the start of the clause:
what perfect predators they really are
Adverbs don't modify nouns and noun phrases. They modify verbs, adjectives, and possibly entire clauses. We can't modify "perfect predators" with "how".
We could modify just "perfect" with an adverb like "very" or "how":
they really are very perfect predators
*they really are how perfect predators
Unfortunately, now we're stuck. Since "how" modifies only "perfect", we want to move "how perfect" to the start of the clause. Since "how perfect" modifies "predators", we don't want to split them up.
If we do move just "how perfect", we end up with something else:
how perfect [that] they really are predators
The result is more naturally parsed as containing a contact clause, and it expresses an entirely different meaning.
If we use another method to separate "how perfect" and "predators", we have something that can be understood:
they really are very perfect as predators
how perfect they really are as predators
On the other hand, "how" could modify the verb or the entire clause. This is even simpler than the case where it modifies an adjective inside a noun phrase:
they really are perfect predators in some manner
*they really are perfect predators how
how they really are perfect predators
The most obvious difference between
what perfect predators they really are
and
how they really are perfect predators
is that the "what" can carry its entire noun phrase to the beginning of the clause, but "how" doesn't carry anything beyond itself. "What" is an adjective, and it needs the thing that it modifies to follow closely behind. "How" is an adverb, and it can modify a verb from a considerable distance.
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* "What" is also a pronoun, but it's a pronoun in the way that many adjectives are.