The correct answer is $\boxed{\text{A}}$, hexanoic acid.
1-hexyne upon treatment with disiamylborane followed by the oxidation with H2O2 gives hexanoic acid. The reaction is as follows:
$$\ce{1-hexyne + disiamylborane -> 1-hexylborane}$$
$$\ce{1-hexylborane + H2O2 -> hexanoic acid + boric acid}$$
The first step of the reaction is the addition of disiamylborane to the 1-hexyne double bond. This reaction is a hydroboration reaction, and it produces 1-hexylborane. The second step of the reaction is the oxidation of 1-hexylborane with hydrogen peroxide. This reaction produces hexanoic acid and boric acid.
Hexanoic acid is a carboxylic acid with the chemical formula $\ce{C6H12O2}$. It is a colorless liquid with a vinegar-like odor. It is the most common fatty acid found in animal fats and oils. It is also used in the production of soaps, detergents, and other chemicals.
The other options are incorrect because they are not produced by the reaction of 1-hexyne with disiamylborane followed by the oxidation with H2O2.