The IUPAC name of given compound is 

Step1-Number of carbon atoms in a straight chain is 8 which means parent alkane is “Octane”. 

Step2-Substituents are given lowest number while numbering in alphabetical order. 

Step3-Functional group is written in the last as suffix, here, it is Ketone which make name as “one” 

Step4-For Alkene lowest position of double bond and “en” is used. 

Step5-Same type of functional group like methyl are assigned number as it is, no preference is required but the position of group and Di, Tri, etc. are used to indicate number of groups present separated by commas. 

Step6-Both compounds with highest priority are on the same side of double bond hence “Z” is assigned. 

Nomenclature of the compound is as (A) (Z)-4,6-Dimethyloct-4-ene-3-one. 

Hence, the correct answer is option (A) (Z)-4,6-Dimethyloct-4-ene-3-one.