Please note that this is not a homework site. We won't do your homework for you. The purpose of homework is that you learn by doing. However we are always willing to help solve problems you encountered, correct mistakes you made in your code and answer your questions.
We didn't see your attempts to solve this problem yourself and so we cannot correct mistakes you didn't made and answer questions you didn't ask. To get help you should do something yourself and get real problems with something. If your problem is "I don't understand a thing", then you should go back to basics and study again.
Furthermore, it is not clear whether your real problem is mathematics or implementation of math with programming language.
Taxicab geometry, considered by Hermann Minkowski in 19th-century Germany, is a form of geometry in which the usual distance function of metric or Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian coordinates.
The taxicab metric is also known as rectilinear distance, ..., Manhattan distance or Manhattan length... The latter names allude to the grid layout of most streets on the island of Manhattan, which causes the shortest path a car could take between two intersections in the borough to have length equal to the intersections' distance in taxicab geometry.