To solve this problem, we need to simplify each expression by combining like terms and fill in the missing pieces in each white rectangle. Here are the solutions for each:

1. Expression 1: $5x - 7x + 10 + 23$

   • Simplified: $-2x + 33$
   • Missing pieces: $-2x$ and 33

2. Expression 2: $6x - 9y - 7x + (-15y)$

   • Simplified: $-x - 24y$
   • Missing pieces: $-x$ and -15y

3. Expression 3: $-14x + x + 25 + 15$

   • Simplified: $-13x + 40$
   • Missing pieces: $-13x$ and 40

4. Expression 4: $3.5x - y + 5.5x - 9x - 4y + 3y$

   • Simplified: $9x - 4y$
   • Missing pieces: $9x$ and $-4y$

5. Expression 5: $-12.3 - 2x + 1.3$

   • Simplified: $-11 - 2x$
   • Missing pieces: $-11$ and $-2x$

6. Expression 6: $\frac{1}{3}x + 2y + \frac{5}{3}x - 4y$

   • Simplified: $2x - 2y$
   • Missing pieces: $2x$ and $-2y$

Would you like to go into further details or have any specific questions?

Here are five related questions to expand your understanding:

1. How do you identify like terms in algebraic expressions?
2. What is the process of combining like terms?
3. How do you handle terms with different signs when combining them?
4. What is the importance of simplifying expressions in algebra?
5. How can you check your work to ensure you have simplified correctly?

Tip: Always group terms with similar variables and constants separately to simplify complex expressions easily.