A road runs along the south boundary of the SW 1/4 of the SW 1/4 of a section. If the road contains two acres in the area, the width of the road would be:

The answer is 66 feet, but I can't calculate it.

a section is 1 mile square

So, each quarter is 1/2 mile on a side.
A 1/4 of a 1/4 is thus 1/4 mile on a side, or 1320 ft

If the road's width is w feet,

1320w = 2*43560
w = 66 ft