Explanation:

To find the 4th proportional to 5, 10, and 12, use the proportion formula. For numbers a, b, c, and d, if a:b = c:d, then b/a = d/c. You can calculate it as follows:

- The ratio of 5 to 10 is 1:2.

- Applying the same ratio to 12, d = (10 × 12) / 5 = 24.

Now, let's check the options:

- Option 1: 8 - This isn't the correct proportional.

- Option 2: 48 - This is too large and not correct.

- Option 3: 20 - This is not correct.

- Option 4: 24 - This matches our calculation.

Therefore, the correct answer is:

Option 4: 24