Number from the end that gives Cl the lowest locant: HOCH₂(1)–CH(2)=C(Cl)(3)–CH(4)=CH(5)–CH₂OH(6), so the name is 3-chlorohexa-2,4-diene-1,6-diol (this rules out options c and d).
C2=C3: on C-2, CH₂OH > H; on C-3, Cl > C-4. CH₂OH and Cl are drawn on the same (lower) side, so this bond is 2Z.
C4=C5: on C-4, C-3 > H; on C-5, CH₂OH > H. C-3 (lower) and CH₂OH (upper) are on opposite sides, so this bond is 4E.
Answer: (2Z,4E)-3-chlorohexa-2,4-diene-1,6-diol (b).