The correct options are
C had moved
D NO CHANGE
Options C and D: The underlined verb form is in present perfect tense. By this, we mean that the action completed in the present.
If we replace the underlined words with 'had moved', the sentence is still complete in meaning. Then, the verb indicates that an action completed in the past. Both the forms of tense are correct, because there is no exact time mentioned, like 'yesterday' or 'today'. Hence both options C and D are correct.
Option A: 'Are' in 'are moving' is a plural verb form. It is used when the noun is also plural. When the noun is singular, the verb is singular. The same goes for plural nouns. But here, 'he' is singular. Hence option A is incorrect.
Option B: 'Moves' is in the simple present tense. This tense indicates a daily habit, or a routine. 'He goes for a walk every morning.' But the given sentence does not state a habit. Hence option B is incorrect.