To solve the given equation using the distributive property, let's break it down step by step:

Given equation:

$4(x - 6) + 6 = 6x - 4$

Step 1: Apply the distributive property to $4(x - 6)$

$4(x - 6) = 4x - 24$ So, the equation becomes: $4x - 24 + 6 = 6x - 4$

Step 2: Combine like terms on the left-hand side

$4x - 18 = 6x - 4$

Step 3: Isolate $x$ terms on one side

Subtract $4x$ from both sides: $-18 = 2x - 4$

Step 4: Solve for $x$

Add 4 to both sides: $-14 = 2x$ Divide both sides by 2: $x = -7$

Final Solution:

$x = -7$

Would you like additional clarification or details on any step? Here are some follow-up questions you might consider:

1. How is the distributive property applied in this equation?
2. Why is it important to combine like terms before isolating $x$?
3. Can we verify the solution by substituting $x = -7$ back into the original equation?
4. What other methods could be used to solve this equation?
5. How does this method generalize to more complex equations?

Tip: Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.