Let's solve the expression step by step:

$-\frac{1}{2} \left( 8 \times 14 \div 2 + 5 - (6 - | -6 |) - 7 \right)$

Step 1: Simplify inside the absolute value

The absolute value of $-6$ is: $| -6 | = 6$ So the expression becomes: $-\frac{1}{2} \left( 8 \times 14 \div 2 + 5 - (6 - 6) - 7 \right)$

Step 2: Simplify inside the parentheses

$6 - 6 = 0$, so: $-\frac{1}{2} \left( 8 \times 14 \div 2 + 5 - 0 - 7 \right) = -\frac{1}{2} \left( 8 \times 14 \div 2 + 5 - 7 \right)$

Step 3: Perform multiplication and division

$8 \times 14 = 112, \quad 112 \div 2 = 56$ So the expression is now: $-\frac{1}{2} \left( 56 + 5 - 7 \right)$

Step 4: Simplify inside the parentheses

$56 + 5 - 7 = 54$ So the expression becomes: $-\frac{1}{2} \times 54$

Step 5: Perform the multiplication

$-\frac{1}{2} \times 54 = -27$

Thus, the value of the expression is:

$\boxed{-27}$

Would you like more details or have any questions about this solution?

Here are 5 related questions:

1. What is the value of $\frac{1}{3}(9 \times 6 - 4 + | -2 |)$?
2. How do you evaluate expressions with absolute values?
3. How does the distributive property work in expressions like $-\frac{1}{2}(a + b)$?
4. What are the rules for performing operations inside parentheses first (PEMDAS)?
5. How does multiplying by a negative fraction affect the result?

Tip: Always solve expressions inside absolute values first before applying any other operations.