Premise : For most people, the left half of the brain controls linguistic capabilities, but some people have their language centers in the right half. When a language center of the brains is damaged, for example, by a stroke, linguistic capabilities are impaired in some way.

Conclusion : Therefore, people who have suffered a serious stroke on the left side of the brain without suffering any such impairment must have their language centers in the right half.

So it needs to assume that damage of linguistic capabilities always cause impairment of language center. It is given in premise and we cannot change the premise. Premise is always true. I have underlined that sentence in the premise. So impairment of language center always accompany damage of linguistic capabilities. But damage of linguistic capabilities not always accompany impairment of language center

So B is wrong as in choice it is given that "Impairment of linguistic capabilities does not occur in people who have not suffered any damage to any language center of the brain". here ii is assuming that damage of linguistic capabilities always accompany impairment of language center

Choice D is correct as in choice it is given that If there are language centers on the left side of the brain, any serious stroke affecting that side of the brain damages at least one of them. It is true as impairment of language center always accompany damage of linguistic capabilities.

Does it help?