Sentence Correction

) In the non underlined part "1984 to 1988" asks for "from" before it and not "between" which requires "X and Y" after it.
Therefore, A and E are incorrect. "between X to Y" is unidiomatic.
B: "After winning..." modifies "injuries" instead of "tennis celebrity Tracy".
C: "the tennis celebrity who" is awkward. Illogically suggests that Tracy Austin won the Open when she was plagued with injuries.
D: Best choice. Hence, D is the answer.
"Plagued by injuries, tennis celebrity Tracy Austin, who won the Italian and U.S. Opens at age 16 in 1979, sat out the years from 1984 to 1988..."
It conveys the intended meaning that Tracy Austin, who now is plagued with injuries, won the Opens at age 16.