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."
But you didn't say anything about orbitals so...
Ehn, sorry, I know I'm no help...