Learn Russian: Там нельзя купить лекарство без рецепта. - You cannot buy medicine without a prescription there.

Because the preposition без (without) always requires the Genitive case. The base word is рецепт, which is a masculine noun ending in a consonant. To form the Genitive singular, we add -а to the end, making it рецепта.

The English translation says "You cannot", but where is the word for "you" in the Russian sentence?

There isn't one! Russian often uses impersonal structures to express general rules. The word нельзя simply means "it is impossible" or "it is not allowed". When used without a specific person, it implies "one cannot" and applies to people in general.

Is the word лекарство in the Nominative or Accusative case here?

It is in the Accusative case because it is the direct object receiving the action of the verb купить (to buy). For neuter nouns ending in -о like лекарство, the Accusative form looks exactly the same as the dictionary form.

Wait, doesn't рецепт mean "recipe"?

Yes, it means both! In Russian, the word рецепт is used for both a cooking recipe and a doctor's medical prescription. Context tells you which one it is, and since this sentence is about buying medicine (лекарство), it means prescription here.