a tricky one I would say again a cause and effect , Strengthen question .

Cause ------------------> Effect

Eruption in 415 ------------> City destroyed .


Now any evidence that shows no other cause is possible for this effect is a winner.

(A) The city of Cephesa is mentioned in a historical work known to have been written in A.D. 400.
[Trap answer , city may have been destroyed earlier and later historical work was written, eliminate]
(B) Coins bearing the image of an emperor who lived around A.D. 410 have been discovered in the ruins of Cephesa, which were preserved by the cinders and ashes that buried the city.
[Seems like a strong contender if the emperor lived in 410 the city certainly survived the eruption on 310. Lets look at other options]
(C) Geological evidence shows that the eruption of Mt. Amnos in A.D. 415 deposited a 10-foot-thick layer of lava on the city of Cephesa.
[Eruption in 415 deposited layer of lave , dose this have any bearing on the how long the city survived , out of scope , eliminate]
(D) Artworks from the city of Cephesa have been found in the ruins of another city known to have been destroyed in A.D. 420.
[Trap answer , art work found in a city that was destroyed in 420 dose not prove that Cephesa survived till 420 , may be some one brought the art work in 310 , eliminate.]
(E) A historical work written in A.D. 430 refers to the eruption of Mt. Amnos in A.D. 415.
[again an out of scope answer , eliminate]

B is clear winner.

we need to give an evidence that suggests that the city was destroyed in 415 AD and not in AD 310, as assumed.

(A) The city of Cephesa is mentioned in a historical work known to have been written in A.D. 400. [a city being mentioned does not add proof to say that the city existed even in AD 400. for example we still talk about harappa and mohenjadaro. so does that mean these ancient cities exist even today? Eliminated!]

(B) Coins bearing the image of an emperor who lived around A.D. 410 have been discovered in the ruins of Cephesa, which were preserved by the cinders and ashes that buried the city. [Bingo! this provides evidence that the city existed in AD 410, thus roviding support for our author's statement]

(C) Geological evidence shows that the eruption of Mt. Amnos in A.D. 415 deposited a 10-foot-thick layer of lava on the city of Cephesa. [how does the thickness of lava layer provide proof that the city was destroyed in 415 AD and not in 310 AD? Eliminated!]

(D) Artworks from the city of Cephesa have been found in the ruins of another city known to have been destroyed in A.D. 420. [The art works could have been traded well before 310 AD. this does not provide evidence to prove that the city was destroyed later. Eliminated!]

(E) A historical work written in A.D. 430 refers to the eruption of Mt. Amnos in A.D. 415. [If an eruption occured, a historical work will refer to it. But from this we cannot conclude that the city was destroyed with this specific eruption only. Eliminated!]

Hope this helps!

(A) Does not strengthen the claim. City may have been destroyed earlier and later historical work was written.
(B) An emperor living around AD410 discovered in the ruins meant there was trade between Cephesa and that other country. If the city was already under ruins in 410, there would have been little chance for coins to get there.
(C) Not important
(D) Does not strengthen claims
(E) Not useful at all. Hence (b).