"How many deaf workers did you hire?"
Translation:Kiom da surdaj laboristoj vi dungis?
Kiom is an adverb, so you can't use it to modify a noun directly. You can say "kiom kostas tio," with kiom modifying the verb kostas directly, but if you want to ask about the quantity of a noun, you have to pair it with "da," the preposition of measure. Think of it as being more like "much" or "many," which you have to pair with how: "how much?" Except those are adjectives, and it's an adverb.
This sentence is confusing me. Consider another sentence from this course:
"La plejparto de germanoj trinkas bieron."
In this case, "de" is used because if it were "da" then the sentence would mean something like, "Their legs, torsos, and arms drink beer, but their heads don't."
In that same sense, I feel like, "Kiom da ...." is saying something like, "Did you hire all of the deaf workers, or just their hands and feet?" I know it sounds silly, but that's what it feels like and I'm having a difficult time understanding why "da" is correct in this sentence, but not in the other.