Let's break down and simplify the expression step by step.

The given expression is:

$-\frac{1}{2} \left( 8 \times \frac{1}{4} \div 2 + 5 - (6 - | -6 |) - 7 \right)$

Step 1: Simplify absolute value $| -6 |$

The absolute value of $-6$ is 6.

So, the expression becomes:

$-\frac{1}{2} \left( 8 \times \frac{1}{4} \div 2 + 5 - (6 - 6) - 7 \right)$

Step 2: Simplify the inner subtraction

$6 - 6 = 0$

Now the expression is:

$-\frac{1}{2} \left( 8 \times \frac{1}{4} \div 2 + 5 - 0 - 7 \right)$

Which simplifies to:

$-\frac{1}{2} \left( 8 \times \frac{1}{4} \div 2 + 5 - 7 \right)$

Step 3: Perform the multiplication and division

First, compute $8 \times \frac{1}{4} = 2$.

Next, divide 2 by 2:

$2 \div 2 = 1$

Now the expression is:

$-\frac{1}{2} \left( 1 + 5 - 7 \right)$

Step 4: Simplify the addition and subtraction

$1 + 5 = 6$ $6 - 7 = -1$

Now the expression becomes:

$-\frac{1}{2} \times (-1)$

Step 5: Multiply

$-\frac{1}{2} \times (-1) = \frac{1}{2}$

Final Answer:

$\frac{1}{2}$

Would you like more details or have any questions? Here are some related problems for practice:

1. Simplify: $-\frac{1}{3} (9 \times \frac{2}{3} - 4 + | -8 | - 2)$
2. Solve: $-\frac{1}{4}(12 \div 3 \times 5 - (4 - | -2 |) + 6)$
3. Evaluate: $\frac{1}{5}(10 - (8 - | -7 |) \div 2 + 3)$
4. Simplify: $-\frac{2}{3} (6 \times \frac{3}{2} - 9 + 5 - | -4 |)$
5. Solve: $\frac{1}{4}(16 \div 2 - (10 - | -9 |) + 7)$

Tip: Always handle absolute values and parentheses first when simplifying complex expressions.