The major product would be 1-bromo-1-chlorocyclohexane due to the better stability of the carbon with the chlorine. The mechanism is the addition of halides.
Work Step by Step
1) The arrow originates from the double bond and points towards H. The bromine leaves with the bonding electrons. 2) The H is attached to the carbon which does not have Chlorine. The carbocation is formed at the carbon with the chlorine. This carbocation is more stable because the chlorine pulls the electrons, making that carbon more electrophilic than the other carbon. 3) Then the $Br^-$ comes and attaches to the carbon with the chlorine, making 1-bromo-1- chlorocyclohexane the major product.