Explanation:

To separate a mixture of sugar and water, the most effective method is evaporation. Here's how it works:

Evaporation:
Evaporation is a process where a liquid changes into its gaseous state. In the case of a sugar-water mixture, the water evaporates, leaving behind the sugar.

1. Heating the mixture: The sugar-water mixture is heated gently. As heat is applied, the water molecules gain energy and begin to move faster. This increased kinetic energy allows the water molecules to escape from the liquid and enter the air as water vapor.

2. Evaporation: As the water evaporates, it separates from the sugar molecules. The sugar molecules are too large to evaporate and remain in the container.

3. Condensation: The water vapor rises and cools down in the air. It then condenses back into liquid water when it comes into contact with a cooler surface, such as the walls of the container or a condenser.

4. Collection: The condensed water droplets are collected, leaving behind the sugar in the original container.

Advantages of Evaporation:
- Evaporation is a simple and cost-effective method to separate sugar and water.
- It does not require any special equipment, making it suitable for everyday use.
- The separated components can be easily collected and used further if desired.

Other Methods:
The other options mentioned in the question are not suitable for separating a sugar-water mixture:

- Filtration: Filtration is used to separate solid particles from a liquid or gas by passing it through a filter. However, in the case of sugar and water, the sugar particles are too small to be effectively filtered, making this method ineffective.

- Separating Funnel: A separating funnel is used to separate immiscible liquids with different densities. It is not suitable for separating sugar and water, as they form a homogeneous mixture with the sugar dissolved in the water.

- Decantation: Decantation is the process of separating a liquid from solid particles by carefully pouring off the liquid, leaving the solid behind. However, in the case of a sugar-water mixture, the sugar is dissolved in the water and cannot be separated by decantation.

Therefore, the correct answer is evaporation for separating a mixture of sugar and water.