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### Problem 6:
Expression: \((6h + 6) + (h - 10)\)

We can simplify this by:
1. Removing the parentheses.
2. Combining like terms.

\[
(6h + 6) + (h - 10) = 6h + h + 6 - 10
\]
\[
= 7h - 4
\]

So, the simplified expression is:
\[
7h - 4
\]

---

### Problem 8:
Expression: \(\frac{1}{2}(4g + 10) + \frac{1}{3}(3g - 6)\)

First, distribute the fractions:
\[
\frac{1}{2}(4g + 10) = \frac{1}{2} \cdot 4g + \frac{1}{2} \cdot 10 = 2g + 5
\]
\[
\frac{1}{3}(3g - 6) = \frac{1}{3} \cdot 3g + \frac{1}{3} \cdot (-6) = g - 2
\]

Now, add the terms:
\[
(2g + 5) + (g - 2) = 2g + g + 5 - 2 = 3g + 3
\]

So, the simplified expression is:
\[
3g + 3
\]

---

Would you like further details on any of these steps?

Here are some related questions you might consider:
1. How do you combine like terms when simplifying algebraic expressions?
2. What are the rules for distributing fractions across terms in parentheses?
3. How do you solve equations involving both variables and constants?
4. Can you solve for \(h\) or \(g\) in the above expressions if given specific values?
5. What happens when you solve these expressions for larger values of \(h\) or \(g\)?

**Tip:** Always distribute carefully when fractions are involved to avoid common mistakes with signs and coefficients.

Simplify the expressions: (6h + 6) + (h - 10) and (1/2)(4g + 10) + (1/3)(3g - 6).

Learn how to simplify algebraic expressions such as (6h + 6) + (h - 10) and (1/2)(4g + 10) + (1/3)(3g - 6) using the distributive property and combining like terms. This detailed step-by-step solution is suitable for students in Grades 7-9.

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