When using a comparative adjective ("-er") "than" is required, so "compared to" is wrong.
Answer (A) & (B) are wrong
We need to be clear on what is/are being compared.
There are two nouns in this question that are eligible for comparison, light (that) and sources (those)
For which noun can we use the comparative adjective "fainter"?
Though,
"Fainter" makes more sense with light,
and the verb detected is more appropriate for "light" than "sources"
Answer choice (C) is wrong. Why? Answer choice (C) is missing subject for the "can be detected...." phrase.
(C) The Hubble Space Telescope will capture
light from sources twenty times
fainter than that [light] can be detected by ground-based instruments.
(C) The Hubble Space Telescope will capture
light from sources twenty times
fainter than that [light] that [light] can be detected by ground-based instruments.
(D) The Hubble Space Telescope will capture light from
sources twenty times
fainter than those [sources] that [sources] can be detected detected by ground-based instruments.
Correct answer (D)Thanks