The equation you provided is:

$4x - 4 = 4x + \square$

It appears you're looking for a value of $x$ that makes this equation true for a specific condition. To solve for $x$, let's isolate it step by step.

Steps to solve:

1. Subtract $4x$ from both sides: $4x - 4 - 4x = 4x + \square - 4x$ This simplifies to: $-4 = \square$
2. Thus, the value of the blank space is $-4$.

This means the equation is true when the blank is replaced by $-4$.

Would you like a more detailed explanation, or do you have other questions about this?

Here are some related questions:

1. How do you solve equations with like terms on both sides?
2. What happens when you have a constant term in an equation?
3. How do you handle equations with variables on both sides?
4. Can this be solved if the blank represents something other than a number?
5. What are some other methods for solving algebraic equations?

Tip: Always try to simplify the equation step by step and isolate the variable to make solving easier.