The problem asks you to expand and simplify the expression:
$7(3w + 2) + 6w$

Steps to solve:

1. Distribute the 7 across the terms inside the parentheses: $7 \times 3w + 7 \times 2 = 21w + 14$

2. Now, add the remaining $6w$: $21w + 14 + 6w$

3. Combine like terms (the terms with $w$): $21w + 6w = 27w$ So, the simplified expression is: $27w + 14$

Final Answer:

$27w + 14$

Let me know if you need further explanation or have additional questions.
Here are 5 related questions to explore:

1. How do you distribute a term over parentheses in an algebraic expression?
2. What are like terms, and how do you combine them?
3. Can you expand and simplify expressions with negative coefficients inside parentheses?
4. How would the result change if the 7 were a negative value, say -7?
5. How do you factor the expression $27w + 14$?

Tip: Always look for like terms when simplifying; it helps to combine terms in a way that reduces the overall complexity of the expression.