Yes, you are correct in saying that the answer would be B) KOCH3 . The base needs to "attack" the H attached to the tertiary center carbon (the carbon with 3 line connected to it). By picking one of those larger bases: there steric hindrance from the greater bulk that reduces reaction efficiency. Moreover, the oxygen's charge in the larger molecules will be a bit more spread out throughout the larger bases, making it less efficiently attack the positively charged H attached to the tertiary carbon.
After the H attack, the previous C-H bond will fold over to the right and form the double C=C bond as the Br leaves as a leaving group all in one step as an E2 elimination reaction.
Let me know if any of this is confusing or if it helps as well!!
