Adding ethanol to louche
Absinthe is a strongly alcoholic beverage containing anethole, which is insoluble in water and very soluble in ethyl alcohol.  When water is added to the absinthe, the alcohol becomes too dilute to keep the anethole dissolved, and it appears milky. When more ethyl alcohol is added in the form of cognac, the solution again becomes strong enough in alcohol to dissolve the anethole and the solution becomes clear again.  

The phrase "stab the fat" is a bit odd, but I'll do my best to explain. Anethole is a fat-like or fat-loving oil, meaning it dissolves well in other fatty sorts of compounds, but not in water (which is lipohpobic, or fat-avoiding/fat-fearing). Ethyl alcohol has two parts to it. One end of it (labeled (fat) in the chemical formula in the question) is lipophilic (attracted to fat) and the other end is hydrophilic (attracted to water). If there is enough alcohol in the mixture, the lipophilic end of the alcohol molecules can surround the anethole ("stabbing the fat") which leaves the other end of the alcohol free to be dissolved in the water (and also any excess hydrophilic portions of the alcohol).  

I hope the "stab the fat" explanation was clear. Don't hesitate to ask for specific clarifications in the comments below.