Translation:Welke Nederlandse woorden ken jij?
I hope someone adds to (or corrects) this, but I suspect either kennen or weten could work here, technically, but they would mean somewhat different things. "Weten" is used, generally, for facts or information. "Kennen" is to have knowledge of or be familiar with something.
Perhaps if I memorized a list of Dutch words, I might know them in the sense of "weten." But if I have learned those words, their definitions, and how to use them, then I know them in the sense of "kennen." And regardless of whether "weten" is possible here, it is this latter sense of familiarity with the words that we mean when we say in English "I know these Dutch words."
Ik weet dat deze woorden Nederlands zijn omdat ik ze ken.