Let's simplify each expression from the given image step by step:

(a) $x + x + y + y$

Combine like terms: $x + x = 2x \quad \text{and} \quad y + y = 2y$ Simplified expression:
$2x + 2y$

(b) $a + a + b + a + b$

Combine like terms: $a + a + a = 3a \quad \text{and} \quad b + b = 2b$ Simplified expression:
$3a + 2b$

(c) $2a + 3a + 4b + 2b$

Combine like terms: $2a + 3a = 5a \quad \text{and} \quad 4b + 2b = 6b$ Simplified expression:
$5a + 6b$

(d) $4x + x + y + 9y$

Combine like terms: $4x + x = 5x \quad \text{and} \quad y + 9y = 10y$ Simplified expression:
$5x + 10y$

(e) $6a + 3b + 2a + b$

Combine like terms: $6a + 2a = 8a \quad \text{and} \quad 3b + b = 4b$ Simplified expression:
$8a + 4b$

(f) $a + 2b + 4a + b + 5a$

Combine like terms: $a + 4a + 5a = 10a \quad \text{and} \quad 2b + b = 3b$ Simplified expression:
$10a + 3b$

Summary of Simplified Expressions:

1. (a) $2x + 2y$
2. (b) $3a + 2b$
3. (c) $5a + 6b$
4. (d) $5x + 10y$
5. (e) $8a + 4b$
6. (f) $10a + 3b$

Do you have any questions or want further clarifications?
Here are some related problems you might enjoy exploring:

1. How can like terms be identified in more complex expressions?
2. Can these simplified expressions be used in equations? If yes, how?
3. What is the importance of combining like terms in algebra?
4. How do coefficients affect the simplification process?
5. How would the simplification change if subtraction was involved instead of addition?

Tip: Always group terms with the same variables and powers together before simplifying!