How can I separate these two alcohols from each other out of the aqueous solution?
I am tasked with separating these two compounds.


If you want to keep both compounds, degrading one of them is obviously not an option.


  They are both solvated in water.


This can be changed - reversibly ;-)

Your left compound is a diol. React the mixture with a ketone in the presence of an acidic catalyst. 

Typically, these reactions are performed to protect ketones by heating them in with ethanediol in toluene in the presence of toluene sulfonic acid. There is no reason not to use it the other way around to protect the diol. 

The reaction product is a cyclic acetal (1,3-dioxolane) which is much less  soluble in water that the parent diol.