The two ways of relating what a person has said are 1)direct and 2)indirect (reported).
In the direct speech, the exact words of the original speaker are repeated.
In the indirect speech (reported speech), the exact meaning of what the speaker told is expressed but not necessarily in the speaker’s exact words.
Option D is correct as the question in the inverted commas is in the simple future tense, the appropriate introductory verb 'asked' is used, and 'would' is used.
Options A, B, and C are wrong as 'said' cannot be used, 'told' is not the appropriate introductory verb, and 'that is not required respectively.
The correct answer is D)She asked when she would know the result of the test.