# How will you convert methyl bromide to dimethylamine?

Well, you can do this in one step; a methyl bromide is not very sterically hindered at all, so a single ${\text{S}}_{N} 2$ reaction with methylamine is sufficient.
By the time the reaction has finished, either the methylamine nucleophile or another molecule of the dimethylamine product would have equilibrated to acquire the proton from the protonated product, since the pKa of methylamine is about $10.66$, while the pKa of dimethyl amine is about $10.73$.