Let's solve the equation:

\[
r - 6 = 6 + 4r
\]

### Steps:
1. Start by moving the \( r \)-terms to one side of the equation. Subtract \( 4r \) from both sides:
\[
r - 4r - 6 = 6
\]
\[
-3r - 6 = 6
\]

2. Move the constant term to the other side by adding 6 to both sides:
\[
-3r = 6 + 6
\]
\[
-3r = 12
\]

3. Now, divide both sides by \( -3 \) to solve for \( r \):
\[
r = \frac{12}{-3}
\]
\[
r = -4
\]

Thus, the solution is \( r = -4 \).

Would you like any more details on how this was solved?

### Follow-up Questions:
1. How can you check if \( r = -4 \) is the correct solution?
2. What if the equation had fractions instead of whole numbers—how would you solve it?
3. How do you approach solving equations with negative coefficients?
4. What happens if the equation involves parentheses and distributed terms?
5. How would the solution change if you added or subtracted the same number from both sides?
6. Can you solve equations with multiple variables differently?
7. What happens when equations have no solution?
8. Could you graph this equation to find the solution visually?

#### Tip: When working with equations, always simplify the equation step by step by eliminating terms systematically from both sides.

Learn how to solve the equation r - 6 = 6 + 4r with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and solving equations. Suitable for students in Grades 7-9.

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