First NBS (N-Bromosuccinimide) always always always is an allylic bromination (in the presence of light & peroxides, or CCl4), so we add Br at an allylic site (Displaces an Alpha hyderogen).
Then KOC(CH)3, being a large, stong, sterically hindered base... undergoes an E2 reaction, kicking off the Br we just added and forming the oh so stable conjugated double bond. Giving 1,3 cyclohexadiene....
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