Solution:
The words from the box are: build, climb, compose, discover, make, invent, paint, write.
Let's correct the sentences:
- Galileo wrote 'Hamlet'. Galileo discovered the moons of Jupiter.
- Shakespeare discovered the moons of Jupiter. Shakespeare wrote 'Hamlet'.
- Mozart built the Eiffel Tower. Mozart composed 'The Magic Flute'.
- Leonardo da Vinci directed 'Ivan the Terrible'. Leonardo da Vinci painted the 'Mona Lisa'.
- Shah Jehan invented dynamite. Shah Jehan built the Taj Mahal.
- Alfred Nobel wrote the song 'Help'. Alfred Nobel invented dynamite.
- Sergei Eisenstein built the Taj Mahal. Sergei Eisenstein directed 'Battleship Potemkin'.
- Gustave Eiffel wrote 'Pride and Prejudice'. Gustave Eiffel built the Eiffel Tower.
- Edmund Hillary and Tenzing Norgay composed The Marriage of Figaro! Edmund Hillary and Tenzing Norgay climbed Mount Everest.
- Marie Curie first climbed Mount Everest. Marie Curie discovered radium.
- John Lennon and Paul McCartney discovered radium. John Lennon and Paul McCartney wrote 'Hey Jude'.
- The novelist Jane Austen painted the 'Mona Lisa'. The novelist Jane Austen wrote 'Pride and Prejudice'.