Final answer:
The influential 20th Century Hungarian composer and music educator in question is Béla Bartók. He was known for incorporating folk music into his compositions and for his work in ethnomusicology. The correct option is d.
Step-by-step explanation:
The influential 20th Century Hungarian composer and music educator referred to in the question is d) Béla Bartók. Béla Bartók was not only a prominent composer but also a remarkable pianist, ethnomusicologist, and teacher.
His work was heavily influenced by folk music, and he collected and analyzed traditional music from Hungary and other countries, significantly contributing to the field of ethnomusicology. Bartók's compositions include orchestral works, string quartets, piano solos, and an opera.
His style was a synthesis of folk music, classicism, and modernism, and he is known for works such as 'Music for Strings, Percussion, and Celesta' and the opera 'Bluebeard's Castle'. The correct option is d.