I see some problems in the first chemical process, the one at the top of the page. One, the reactant is hexane, not hexane (which is what you drew). Two, bromine is neutral, but what you drew looks like bromide ion, which has a negative charge (I could be misinterpreting what you wrote). Three, if bromide ion removed a proton from hexane (which isn't likely), then the carbon that remained would be negatively charged, not positively charged.
Two of the three reactions (the one in CCl4 without light and the one in water) proceed through the same intermediate, but the intermediate leads to different products in the two different solvents. The alkene and Br2 react to form this intermediate by displacing one bromine atom in the form of bromide ion. The positively charged intermediate that forms in the first step has three atoms, the two carbon atoms from the double bond of hexane and one bromine. Could you try to draw it? You can draw it in such a way that all atoms have a Lewis octet of electrons. Once you get this intermediate, the two products become very easy to see.