Solving the equation 2(ax - by) + 4b = 0 using cross multiplication involves expanding the equation, rearranging the terms, and solving for the variables. Here's a step-by-step explanation:

Expanding the equation:
1. Start with the equation: 2(ax - by) + 4b = 0
2. Distribute 2 to both terms inside the parentheses: 2ax - 2by + 4b = 0

Rearranging the terms:
3. Rearrange the equation to group like terms together: 2ax + 4b - 2by = 0
4. Combine the constants: 4b = -2ax + 2by
5. Divide both sides of the equation by 2 to simplify: 2b = -ax + by

Solving for the variables:
6. To solve for 'x', isolate 'x' on one side of the equation:
-ax = 2by - 2b
Divide both sides by '-a': x = (2b - by) / a

7. Similarly, to solve for 'y', isolate 'y' on one side of the equation:
by = 2b - ax
Divide both sides by 'b': y = (2 - ax) / b

The final solution:
The solutions for 'x' and 'y' are:
x = (2b - by) / a
y = (2 - ax) / b

These equations provide the values of 'x' and 'y' that satisfy the given equation. To find the numerical values, substitute the appropriate values of 'a' and 'b' into the equations and simplify further if needed.

Note: Cross multiplication is a method commonly used to solve linear equations involving fractions or variables on both sides. It helps to isolate the variable by multiplying both sides of the equation by a common denominator. However, in this case, cross multiplication is not necessary since the equation does not involve fractions or variables on both sides.