Homogeneous mixtures are uniform throughout, meaning that the components are evenly distributed and not visibly distinguishable. In option 1, starch and sugar are two different substances that can be easily distinguished, so it is not a homogeneous mixture. Similarly, in option 3, graphite and charcoal are two distinct forms of carbon, making it a heterogeneous mixture.

The correct answer is option 2: Methanol and water. Methanol and water can form a homogeneous mixture because they are both liquids and can dissolve in each other completely. When mixed, methanol molecules and water molecules are evenly distributed, resulting in a uniform solution.

Option 4, calcium carbonate and calcium bicarbonate, is not a homogeneous mixture. These compounds are solid and cannot dissolve in each other. When combined, they will not form a uniform mixture and can be visually separated.

Therefore, the correct answer is option 2, and the explanation shows that it is the only choice that fits the definition of a homogeneous mixture.