Learn French: Quoi que vous fassiez, cet incident provoque un préjudice. - Whatever you do, this incident causes damage.

It depends on the meaning! Quoi que (two words) means "whatever" or "no matter what," which fits this sentence. However, quoique (one word) means "although" or "even though." They both require the subjunctive, so you have to choose the spelling based on the translation you need.

Why do we use the subjunctive fassiez instead of the indicative faites here?

The expression quoi que always triggers the subjunctive. This is because it sets up a hypothetical or undetermined situation: you are referring to absolutely anything the person might do, rather than a specific, established fact.

Does préjudice mean "prejudice" in the sense of a bias or discrimination?

No, préjudice is a classic false friend. In French, un préjudice means "damage," "harm," or "loss" (often used in legal, professional, or formal contexts). If you want to say "a prejudice" (a bias), you should use the word un préjugé.

Why doesn't the subjunctive carry over to the verb provoque?

The subjunctive is only triggered inside the dependent clause introduced by quoi que. The main clause (cet incident provoque un préjudice) states an objective reality—the damage is a fact—so it remains in the normal present indicative.