Why Is the Delta G Positive in Hydrophobic Interaction with Water?

[lha08]

Homework Statement

So like let's say oil and water are interacting together. I know that they do not readily interact together and so water aggregates in a more ordered state around the oil.
But then this is where I'm confused;
-They say that the delta G (change in free energy) is positive, so that means free energy is required. Do they mean the energy is required to make the water molecules into a more ordered state?
-Then they apparently the delta H (change in enthalpy) is negative, because the reaction is exothermic...like I am confused...if the free energy is positive and requires free energy, wouldn't the delta H be positive indicating an endothermic reaction?

Homework Equations

The Attempt at a Solution

 

[Mapes]

Who says that $\Delta G>0$ when an oil-water mixture separates? It happens spontaneously, so the Gibbs free energy must decrease.