After eating a meal, I will take the hospital's medicine. [Syntax]

The correct answer is "薬(くすり)" (kusuri). This sentence describes taking something after a meal. "ご飯(はん)を食(た)べた後(あと)で" (after eating a meal) sets the timing. The action is "飲(の)みます" (to drink/take). "病院(びょういん)の" means "of the hospital". The most logical item to take/drink from a hospital is "薬(くすり)" (medicine). Therefore, "病院(びょういん)の薬(くすり)を飲(の)みます" correctly means "I will take the hospital's medicine". "病院(びょういん)" and "の" are already in the sentence, modifying the object. "を" is the object particle and comes after the object itself.