Answer :

To determine the most appropriate unit for measuring the distance around the world at the equator, let's consider the magnitude of each unit compared to the actual distance.

1. Meters (a):
- One meter is a relatively small unit. 42,000 meters would be an unrealistically short distance for the circumference of the Earth.

2. Kilometers (b):
- One kilometer is 1,000 meters, so 42,000 kilometers is a large distance suitable for measuring the circumference of the Earth. This is a realistic and appropriate unit as the Earth's equatorial circumference is approximately 40,075 kilometers.

3. Centimeters (c):
- One centimeter is extremely small, and measuring the equatorial distance of the Earth in centimeters would result in an impractical and huge number. Specifically, 42,000 kilometers in centimeters would be 4,200,000,000 centimeters, which is cumbersome.

4. Millimeters (d):
- One millimeter is even smaller than a centimeter. Using millimeters to measure the Earth's circumference would result in an extraordinarily large number (42,000 kilometers would be 42,000,000,000 millimeters), which is not practical.

Based on these considerations, the most appropriate unit for measuring the distance around the world at the equator is kilometers.

Therefore, the correct choice is:

b. kilometers