Final answer:
Tom used 2/3 of a box of nails for 1/4 of his fence. To finish the rest of the fence, which is three times the amount completed, he will need three times the nails, amounting to 2 full boxes.
Step-by-step explanation:
Considering that Tom built 1/4 of his fence using 2/3 of a box of nails, we can infer that to build the entire fence, we'd need four times the amount of nails used for 1/4 of the fence. This is because 1/4 is one part of four equal parts that make up a whole. Since 2/3 of a box was used for 1/4, multiplying that fraction by 4 gives us (2/3) * 4 = 8/3, which simplifies to 2 and 2/3. However, since Tom already used 2/3 for the first quarter, he will only need 8/3 - 2/3 = 6/3 or 2 boxes of nails to finish his fence.