What would be the major products of this reaction? Obviously, A would be 3-Bromoo 3-methyl cyclo hexene:

as the stable free radical intermediate would be formed.
But B is what I am having problems with. I read that $\ce{LiAlH4}$ forms alkenes with three degree halides. So my guess was
2-Methyl-1,3-cyclohexadiene:


But when I checked my book, it said B would just be the Bromine getting substituted by Deuterium in (A)
(I'm sorry I don't know any site that allows making chemical structures with isotopes included so I had to describe it like this.)
Can someone please help me out with this?
I will give this my best shot. There doesn't appear that there is any conclusive evidence for this reaction since some sources say elimination is favoured while others say substitution is the major product. However, for this reaction, the difference likely resides in the fact that it is an allylic bromide. This is extremely favourable for substitution reactions because the intermediate will be very stable. Just because of that, substitution may be favoured over elimination and result in the major product being Br substituted for a deuterium atom, just as your book mentioned.