Final answer:
For a trench 3 feet deep, 6 times the original product amount is needed, resulting in a total of 24 gallons, corresponding to answer choice D.
Step-by-step explanation:
If a 6 inches wide by 6 inches deep trench requires 4 gallons per 10 linear feet for treating subterranean termites, we need to determine how much product to use for a 3 feet deep trench. Since the trench depth is multiplied by 6 to get from 6 inches to 3 feet (1 foot = 12 inches), we would expect to need 6 times the product if all other dimensions remain proportional.
However, because the trench's width is not specified to change, we need to be careful. Trench volume depends on both depth and width, but in this question, we only have information about the depth changing.
Since the amount of product corresponds to the volume of the trench that it fills, and this volume has increased by a factor of 6 (from 6 inches to 3 feet), we can calculate the required product by multiplying the provided 4 gallons by 6.
Therefore, the amount of product needed is 4 gallons (original amount for 6 inch depth) multiplied by 6, which equals 24 gallons. This corresponds to answer choice D.