That would be a chemical reaction of ethene with water (usually an acid-catalyzed reaction), but the final product is CH3CH2OH.
This is not a typical biochemical reaction involving ethanol, though. More typical would be the ADH-catalyzed reduction of acetaldehyde to ethanol with NAD as a required co-factor. (ADH = alcohol dehydrogenase)
Should also point out that the chemical reaction you’ve listed is OK, but it is really an equilibrium. Once you accumulate an amount of ethanol, you will start to see the reverse reaction: acid-catalyzed hydrolysis of an alcohol to generate an alkene.