HNMR - Peak Splitting
Both are correct to some degree.

The first book predicting 12 lines is being very theoretical.  In principle with narrow enough line widths 12 lines would be observed.  However, due to coupling constants (J) being similar from the beta protons to the alpha and gamma protons, in practice with reasonable resolution, only 6 lines are observed (the first book is actually explaining this in fine print).


(source: ucalgary.ca)  

Credit: Univ. Calgary