The conversion of sugar into carbon dioxide gas ($C{O}_2$) and ethyl alcohol is carried out by yeast cells. What is this process called?

The correct option is A Fermentation

Fermentation is a metabolic process that converts sugarto acids, gases or alcohol. It occurs in yeast and bacteria, but also in oxygen-starved muscle cells, as in the case of lactic acid fermentation.
$\underset{Glucose}{C_6{H}_{12}{O}_6}\to \underset{Ethanol}{2C_2{H}_{5}OH}+\underset{CarbonDioxide}{2C{O}_2}+Heat$
Fermentation does not require oxygen. If oxygen is present, some species of yeast will oxidizepyruvate completely to carbon dioxide and water.