The subject is 'dating' so the verb has to be the plural 'suggests', which brings us to C, D and E.

The subjunctive mood states that 'suggest' should always be followed by 'that'. Hence C is the correct answer.
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Radiocarbon dating of fossils taken from caves on islands along southeastern Alaska's coast suggest that at least a portion of the area was remaining ice-free during the last ice age.

a. suggest that at least a portion of the area was remaining There are 2 issues with this answer option:

i) What "suggests"? Radiocarbon dating. Therefore the subject of the verb "suggest" is singular, requiring the singular verb "suggests".
ii) The usage of the past continuous tense "was remaining" is problematic. Past continuous tense is used to emphasise the progress of an event in the past, often to overlap with a second event which is normally expressed in simple past tense (eg; Alan was cutting the grass the other day when the snake appeared). In this case, there is no second event, hence, it not clear why a past continuous tense is required. This is not a hard and fast rule (eg; "Alan was cutting the grass." is a perfectly acceptable sentence, although we can guess that there something else going on in the larger context, a second event), but a simple past expression is more concise and simpler.

b. suggest at least a portion of the area remaining Same subject-verb mismatch as explained in (i) above. Also, subjunctive mood "suggests" should be followed by "that".

c. suggests that at least a portion of the area remained Correct.

d. suggests at least a portion of the area that had remained Now here there is no ambiguity - the past perfect tense "had remained" necessitates a second event, since past perfect is used to show the order of happening of two events in the past. Incorrect. Also, subjunctive mood "suggests" should be followed by "that".

e. suggests at least a portion of the area to have remained. Two issues with this option:

i) Subjunctive mood "suggests" should be followed by "that".
ii) Present perfect "have remained" implies that the action (or its impact) continues till the present, which is an extrapolation of the sentence given in the question - a meaning shift.

Hope this helps.
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