[sharbeldam]

The question basically says which enolate is more stable a/b/c/d
Now it's a bit confusing because it says " Z more stable " on the right of the molecule but as i look at it, should not that molecule be E? since the R group on the next carbon is opposite to the O-?

[sharbeldam]

https://media.cheggcdn.com/media%2Fd66%2Fd6684739-9e6b-4f73-b55f-c8a988079ad2%2Fimage

its basically the same question, i do realize that the conjugated double bonds should be more stable, that means its either C or D, but how can we decide which one is it? Z or E enolate? and what is the definition of E/Z enolate? is it the relation between the R group on one carbon with the Oxygen ion on the other carbon?

[hypervalent_iodine]

I believe you are correct in saying that they have given the incorrect E/Z assignment. 

There are a few factors that govern which configuration is more stable. Very broadly, when your R groups are small you will typically get the E configuration. When one or both are large, you tend to get the Z configuration. I believe there is a Kahn Academy video on this somewhere, but failing that, these slides give a nice overview. http://www.massey.ac.nz/~gjrowlan/stereo2/lecture7.pdf