To find the time when Tom and Ben meet each other, we can use the formula:

Time = Distance / Speed

The total distance between Tom's house and Ben's house is 36 km. Since they are cycling in opposite directions, the distance each person travels can be calculated as half of the total distance, which is 18 km.

For Tom:
Time = 18 km / 6 m/s = 3 hours

For Ben:
Time = 18 km / 4 m/s = 4.5 hours

Since they started at 1.00 P.M., Tom and Ben will meet each other after 3 hours, which is at 4.00 P.M.

Therefore, the correct answer is B. 4 P.M.