1. Let's clarify the problem: You are asking why we divide an expression by $4x$ when the expression contains $4y$. 2. Typically, division by $4x$ is done to isolate a variable or simplify an equation. 3. For example, if we have an equation like $4xy = 8$, dividing both sides by $4x$ helps us solve for $y$: $$\frac{4xy}{4x} = \frac{8}{4x}$$ 4. Using the cancellation rule, we get: $$\frac{\cancel{4x}y}{\cancel{4x}} = \frac{8}{4x}$$ 5. This simplifies to: $$y = \frac{8}{4x}$$ 6. Then, simplifying the fraction: $$y = \frac{8}{4x} = \frac{8 \div 4}{4x \div 4} = \frac{2}{x}$$ 7. So, dividing by $4x$ is a step to isolate $y$ by removing the coefficient $4x$ attached to it. 8. This is a common algebraic technique to solve for a variable when it is multiplied by other terms.