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I can see the set of problems provided. Let's solve each of them step by step, showing the complete solution.

### Problem 11: 
\[ 2 + 5 \cdot 4 + 3 \cdot 6 \]

**Solution:**
- Follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. First, handle the multiplications:
   \[
   5 \cdot 4 = 20
   \]
   \[
   3 \cdot 6 = 18
   \]
   
2. Now add them in sequence:
   \[
   2 + 20 + 18 = 40
   \]
   
**Answer:** \( 40 \)

---

### Problem 12:
\[ 12 - 3 \cdot (2 + 7) + 8 \cdot (7 - 2 \cdot 1) \]

**Solution:**
1. Simplify inside parentheses first:
   \[
   2 + 7 = 9
   \]
   \[
   7 - 2 \cdot 1 = 7 - 2 = 5
   \]
   
2. Perform the multiplications:
   \[
   -3 \cdot 9 = -27
   \]
   \[
   8 \cdot 5 = 40
   \]

3. Now add/subtract in sequence:
   \[
   12 - 27 + 40 = 12 + 13 = 25
   \]
   
**Answer:** \( 25 \)

---

### Problem 13:
\[
\frac{-14}{5 - (-2)}
\]

**Solution:**
1. Simplify the denominator:
   \[
   5 - (-2) = 5 + 2 = 7
   \]
   
2. Now divide:
   \[
   \frac{-14}{7} = -2
   \]
   
**Answer:** \( -2 \)

---

### Problem 14:
\[
-6(2x + 3y) - [3x - (2 - 5y)]
\]

**Solution:**
1. Distribute the \( -6 \) in the first term:
   \[
   -6(2x + 3y) = -12x - 18y
   \]

2. Simplify inside the bracket:
   \[
   3x - (2 - 5y) = 3x - 2 + 5y
   \]

3. Now subtract the bracketed term from the first term:
   \[
   (-12x - 18y) - (3x - 2 + 5y) = -12x - 18y - 3x + 2 - 5y
   \]

4. Combine like terms:
   \[
   -12x - 3x = -15x
   \]
   \[
   -18y - 5y = -23y
   \]

   The constant term remains \( +2 \).

**Answer:** \( -15x - 23y + 2 \)

---

### Problem 15:
\[
2 - 3[(4x - 5) - 3x - 7]
\]

**Solution:**
1. Simplify inside the bracket:
   \[
   (4x - 5) - 3x - 7 = 4x - 3x - 5 - 7 = x - 12
   \]

2. Now distribute the \( -3 \):
   \[
   2 - 3(x - 12) = 2 - 3x + 36
   \]

3. Simplify:
   \[
   2 + 36 - 3x = 38 - 3x
   \]

**Answer:** \( 38 - 3x \)

---

Let me know if you want details or have any questions! 

### 5 Related Questions:
1. What is the correct order of operations for solving complex expressions?
2. How does distribution work when dealing with negative signs?
3. What is the difference between adding and subtracting negative terms in expressions?
4. How do you simplify algebraic expressions involving parentheses?
5. What happens when you subtract a negative number from another negative number?

### Tip:
Always evaluate expressions inside parentheses first before handling any other operations, especially when negative signs or distributions are involved.

Solve the math expression 2 + 5 * 4 + 3 * 6 by applying the correct order of operations. This problem focuses on multiplication and addition using PEMDAS. Suitable for students in Grades 6-8.

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