I'm not sure what it is you're asking so maybe I shouldn't be replying.... I'm only in high school level chem
So you know that violates the octet rule, right? Carbon would have to form a quadruple bond with another carbon in order for it to be right in terms of the octet rule... but according to wikipedia that doesn't usually happen.
For your diagram, the unbonded electrons aren't paired, the way I've been doing it with Lewis dot diagrams, that part's right....
oh, and... wikipedia has this to say: "Carbon atoms can also form double bonds called alkenes or triple bonds called alkynes. A double bond is formed with an sp2 hybridized orbital and a p-orbital that isn't involved in the hybridization."
I don't want to complicate things for you because I don't know where you are in your course but generally, elections don't move that way. I think you're book is just trying to sample what you will be learning much farther along the course. Before you learn how to form double bonds, you must first learn how to form single bonds. Before you learn how to form single bonds, you must know the meaning of an electrophile and nucleophile. If you can't represent that on a drawing then it really has no meaning but if that's what you're book is showing you right now then just go with it.