To solve this problem, we need to consider the different possibilities for choosing a black square that does not lie in the same row as the white square. Let's break down the solution into different steps:

Step 1: Understanding the chessboard
A standard chessboard consists of 8 rows and 8 columns, resulting in a total of 64 squares. The rows are labeled from 1 to 8, and the columns are labeled from a to h. Each square can be identified by its row number and column letter. For example, the square in the first row and first column is denoted as a1, while the square in the eighth row and eighth column is denoted as h8.

Step 2: Choosing a white square
There are 32 white squares on the chessboard. Since we are choosing a white square at random, each white square has an equal probability of being chosen.

Step 3: Choosing a black square in a different row
If we choose a white square, we need to find the number of black squares that do not lie in the same row as the white square. Since there are 8 rows on the chessboard, there are 7 other rows that the black square can be chosen from.

Step 4: Calculating the total number of possibilities
To calculate the total number of possibilities, we multiply the number of white squares by the number of black squares in a different row. Therefore, the total number of possibilities is 32 (number of white squares) multiplied by 7 (number of black squares in a different row) which equals 224.

However, the question asks for the number of ways, not the total number of possibilities. So, we need to consider the different ways of choosing a white square and a black square in different rows.

Step 5: Considering the different ways of choosing a white and black square
We know that there are 32 white squares and 7 rows from which we can choose a black square. For each white square, there are 7 possible choices for the black square. Therefore, the total number of ways of choosing a white square and a black square in different rows is 32 multiplied by 7, which equals 224.

Step 6: Comparing with the given options
The correct answer is option D, which is 2002. This does not match the value we calculated (224). Therefore, the given answer is incorrect, and there might be a mistake in the question or answer options.

In conclusion, the correct number of ways to choose a black square such that it does not lie in the same row as the white square is 224, not 2002 as mentioned in option D.