Option 1 -> Creates grammatical disconnect, interrupting the flow between parts A and D.
Option 2 -> Places the identification of who Rubik is at the end, making the sentence structure awkward.
Option 3 -> Starts with a prepositional phrase without proper subject, creating incomplete meaning.
Option 4 -> Begins with the identification (D), flows into the relative clause about Erno Rubik (A), completes the object "puzzle" (C), and ends with the purpose "concepts of three dimensional movements" (B).
Hence, Option 4: (D), (A), (C), (B) -> This arrangement creates a grammatically correct and logical sentence: "The 'Rubik' in Rubik's Cube is a Hungarian professor of architecture Erno Rubik, who first created his twisty mechanical puzzle to teach his students the concepts of three dimensional movements." -> correct