How do plants convert sugars into fats?

Answer

This requires a lot of biochemical reactions.
In glycolysis (a biochemical process in 10 steps that converts glucose sugar into pyruvic acid), dihydroxyacetone phosphate is released in one of the steps. Glycerol can be formed with this. Fatty acids can be made from pyruvic acid. Fatty acids and glycerol are the building blocks of lipids (= fats or oils).
The production of fats or oils in seeds and fruits is a way to store energy. In seeds and fruits, that oil is stored in cell organelles called elaioplasts.