If a radioactive substance has a half-life of four months, it means that in every four-month period, half of the substance will decay.

To determine the time it takes for three-fourths (3/4) of the substance to decay, we need to consider the number of half-lives required.

After the first half-life (four months), half of the substance remains (1/2).

After the second half-life (eight months), half of the remaining substance remains (1/2 * 1/2 = 1/4).

After the third half-life (12 months), half of the remaining substance remains (1/4 * 1/2 = 1/8).

Since three-fourths of the substance would decay, we are interested in the point where 1/4 of the substance remains (after the second half-life). Therefore, the substance would decay three-fourths in 8 months.

Thus, the correct answer is 8 months.