What is the DOMINANT organic product of the reaction of 2,3-Dimethyl-1,3-butadiene with two (2) moles of Br2?
I can draw and know what 2,3-Dimethyl-1,3-butadiene looks like but have no idea where the Br2 is going to bond at, also does the two moles of Br2 matter?
For the mechanism, the first step is nucleophilic attack resulting in electrophilic addition (where the pi bond acts as the nucleophile); the second step is nucleophilic attack resulting in nucleophilic addition (where the Br- (or OH- if aqueous conditions are used) acts as the nucleophilie).
Four points to consider :
1) The solvent used matters. With a non-polar, inert solvent, you'll get the addition of bromine only. Using aqueous bromine, you have a competing hydroxide ion nucleophile that will attack the cyclic bromonium carbocation intermediate, in effect adding not just Br, but also OH, across the double bonds.
2) If we regard the cyclic bromonium ion as a non-cyclic carbocation, (eg. imagine you're adding H-Br instead of Br-Br), then the more stable carbocation would be the one with more electron donating (non-electronegative-substituted) alkyl groups. If both double bonds are added across simultaneously, and based on this argument alone, you would end up with 1,4-dibromo-2,3-dihydroxy-2,3-dimethyl-butane.
3) However, because oxygen is significantly more electronegative than bromine, the resulting electronic instability of 1,4-dibromo-2,3-dihydroxy-2,3-dimethyl-butane (with the two partial +ve Cs being adjacent), may see the emergence of 2 other slightly more stable isomers (at least in regard to the two partial +ve adjacent Cs), 1,3-dibromo-2,4-dihydroxy-2,3-dimethyl-butane and 2,3-dibromo-1,4-dihydroxy-2,3-dimethyl-butane.
4) Let's consider sterics. Br is huge, but OH is small. But Br has to be added on first, since the pi-bond acts as a nucleophile (and attacks the +ve charged Br). So the next step of OH- nucleophile attacking the carbocation (or bromonium carbocation), might preferentially add on to the terminal C's, to minimize steric repulsion (or van der Waals repulsion), so this argument tends towards the isomer 2,3-dibromo-1,4-dihydroxy-2,3-dimethyl-butane.
The answer (single major product) isn't directly provided by this post, but hopefully these 4 points above might have possibly helped you understand the processes or considerations involved a little better.