Simplify algebraic expressions by combining like terms.

To simplify the given expressions, we need to collect and combine like terms. Like terms are terms that have the same variable(s) raised to the same power. Let's solve each expression step by step.

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a) \( 2x + 6y + 7x \)

- Combine the \( x \)-terms: \( 2x + 7x = 9x \)
- The \( y \)-term remains as it is: \( 6y \)

So, the simplified expression is:
\[
\boxed{9x + 6y}
\]

---

b) \( 3a + 8b + 5a \)

- Combine the \( a \)-terms: \( 3a + 5a = 8a \)
- The \( b \)-term remains as it is: \( 8b \)

So, the simplified expression is:
\[
\boxed{8a + 8b}
\]

---

c) \( 6u + 3v - 2u \)

- Combine the \( u \)-terms: \( 6u - 2u = 4u \)
- The \( v \)-term remains as it is: \( 3v \)

So, the simplified expression is:
\[
\boxed{4u + 3v}
\]

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d) \( 9p + 8q - p \)

- Combine the \( p \)-terms: \( 9p - p = 8p \)
- The \( q \)-term remains as it is: \( 8q \)

So, the simplified expression is:
\[
\boxed{8p + 8q}
\]

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e) \( 2m + 5n + 4m + 3n \)

- Combine the \( m \)-terms: \( 2m + 4m = 6m \)
- Combine the \( n \)-terms: \( 5n + 3n = 8n \)

So, the simplified expression is:
\[
\boxed{6m + 8n}
\]

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f) \( 6u + 9v + u + 3v \)

- Combine the \( u \)-terms: \( 6u + u = 7u \)
- Combine the \( v \)-terms: \( 9v + 3v = 12v \)

So, the simplified expression is:
\[
\boxed{7u + 12v}
\]

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g) \( 8b + 7c + 3b - 2c \)

- Combine the \( b \)-terms: \( 8b + 3b = 11b \)
- Combine the \( c \)-terms: \( 7c - 2c = 5c \)

So, the simplified expression is:
\[
\boxed{11b + 5c}
\]

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h) \( a + 2b + a - b \)

- Combine the \( a \)-terms: \( a + a = 2a \)
- Combine the \( b \)-terms: \( 2b - b = b \)

So, the simplified expression is:
\[
\boxed{2a + b}
\]

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i) \( 5a + 2b - 5a + 6b \)

- Combine the \( a \)-terms: \( 5a - 5a = 0 \)
- Combine the \( b \)-terms: \( 2b + 6b = 8b \)

So, the simplified expression is:
\[
\boxed{8b}
\]

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j) \( 9p + 3q - 2p - 3q \)

- Combine the \( p \)-terms: \( 9p - 2p = 7p \)
- Combine the \( q \)-terms: \( 3q - 3q = 0 \)

So, the simplified expression is:
\[
\boxed{7p}
\]

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Final Answers:

\[
\boxed{
\begin{aligned}
&\text{a) } 9x + 6y \\
&\text{b) } 8a + 8b \\
&\text{c) } 4u + 3v \\
&\text{d) } 8p + 8q \\
&\text{e) } 6m + 8n \\
&\text{f) } 7u + 12v \\
&\text{g) } 11b + 5c \\
&\text{h) } 2a + b \\
&\text{i) } 8b \\
&\text{j) } 7p
\end{aligned}
}
\]