Through which process is energy transferred to a molecule that the cell can use as fuel for its various activities?

The process is called respiration. Cells in our bodies uses respiration to break up food molecules such as sugars into a form that the cells use as energy. The food we eat undergoes digestion where it is broken down to its monomer unit e.g. starch is broken down to its glucose units which are also called simple sugars. Glucose is taken from the digestive system and into cells where it undergoes glycolysis in the cytoplasm to make pyruvate. Pyruvate is transferred into the mitochondria of the cell where it passes into the citric acid cycle to produce ATP. ATP is the form of energy that our cells use to function.

Very hard to understand