To solve the equation $9(x - 4) = 2(x + 3)$, follow these steps:

1. Distribute the 9 and the 2: $9x - 36 = 2x + 6$

2. Move all terms involving $x$ to one side of the equation and constants to the other side. Subtract $2x$ from both sides: $9x - 2x - 36 = 6$ Simplify: $7x - 36 = 6$

3. Add 36 to both sides to isolate the term with $x$: $7x - 36 + 36 = 6 + 36$ Simplify: $7x = 42$

4. Divide both sides by 7 to solve for $x$: $x = \frac{42}{7}$ Simplify: $x = 6$

So, the solution to the equation is $x = 6$.

Would you like more details or have any questions?

Here are some related questions:

1. What if the equation was $9(x - 4) = 2(x + 3) + 10$?
2. How do you solve $5(x - 2) = 3(x + 4)$?
3. What steps would you take to solve $8(x + 5) = 4(x - 2)$?
4. How can you verify the solution $x = 6$ is correct for the original equation?
5. What if the equation was $9(x - 4) = 2(x + 3) + x$?
6. How do you solve $12(x - 3) = 4(2x + 1)$?
7. What is the solution to $7(x + 2) = 5(x + 6)$?
8. How do you solve $3(x - 1) = 6(x - 2)$?

Tip: When solving linear equations, always simplify both sides of the equation first and then isolate the variable on one side.