Let's simplify the given mathematical expression step by step:

$2 \times | -15 - (-8) | + (-12)$

Step 1: Simplify the expression inside the absolute value

$-15 - (-8) = -15 + 8 = -7$

Step 2: Take the absolute value

$| -7 | = 7$

Step 3: Multiply by 2

$2 \times 7 = 14$

Step 4: Add $-12$

$14 + (-12) = 14 - 12 = 2$

Final Answer:

$\mathbf{2}$

Would you like a detailed breakdown of any step?

Here are some related questions you might find helpful:

1. How do absolute values affect negative numbers in expressions?
2. What are the properties of absolute value operations?
3. How do parentheses change the order of operations?
4. How can you simplify expressions with multiple operations?
5. What happens if the absolute value contains variables instead of numbers?

Tip:

Always solve the innermost parentheses first before dealing with absolute values!