Learn Icelandic: Hvorugur strákanna veit svarið. - Neither of the boys knows the answer.

Hvorugur specifically means "neither of two". This ties into the dual vs. plural lesson: just as hvor means "which of two", hvorugur is used when there are exactly two options or people. If there were three or more boys, you would use enginn (none) instead.

Why is strákanna in the genitive case here?

Words that pick out a specific number from a larger group—like "neither of", "one of", or "some of"—take the genitive case in Icelandic. So, strákanna literally translates to "of the boys".

If we are talking about "the boys" (strákanna), why is the verb veit in the singular form?

The main subject of the sentence is actually Hvorugur (neither one), which is grammatically singular. The verb veit agrees with Hvorugur, not the plural group the boys belong to. This is just like in English where we say "neither knows" instead of "neither know".

Could I use þekkir instead of veit for "knows" in this sentence?

No, because vita (the dictionary form of veit) is used for knowing facts, information, or answers. You use þekkja when you are talking about being familiar with a person, place, or thing. Since they do not know "the answer" (svarið), veit is the right choice.