I believe that your correct answer would be "This sentence shows Elion's determination and commitment to learn."
The reason why I say this is because Elion wanted to be a "biochemistry". But she could not because of her requirement's are not that great. She took many classes and so on and still could not qualify.She needed to learn to have determination.she didn't earn a doctorate so the 1st sentence is false,
she didn't get denied going to any schools so the 3rd one is also false.
she earned her degree at the first college so the 4th one is also false.
the correct answer should be:
This sentence shows Elion's determination and commitment to learn.