Why does (3E)-3,4-dimethylhex-3-ene yield a meso dihalide when reacted with Br2/CCl4 at room temperature?
A meso compound is a molecule with multiple stereocenters that is superimposable on its mirror image. Meso compounds are easily identified by their internal plane of symmetry.

Using this knowledge, and given that $\ce{Br2}$ undergoes anti addition to alkenes, there are only really two answers that could possibly be meso compounds, B and D. Let us consider the products:



Notice how only B has an internal plane of symmetry, and is therefore a meso compound.