The expression given is:

$2 \left( 2.5 - | -6 | \right)$

Step 1: Simplify the absolute value

The absolute value of $-6$ is $6$, because absolute values remove the negative sign:

$| -6 | = 6$

Now, substitute this back into the expression:

$2 \left( 2.5 - 6 \right)$

Step 2: Perform the subtraction inside the parentheses

Now, calculate:

$2.5 - 6 = -3.5$

So, the expression becomes:

$2 \times (-3.5)$

Step 3: Multiply

Now, multiply:

$2 \times (-3.5) = -7$

Thus, the simplified expression is:

$\boxed{-7}$

Would you like more details on any step?

Here are some related questions you might consider:

1. What are the properties of absolute value functions?
2. How do we handle operations with negative numbers?
3. What are the rules for multiplying with negative numbers?
4. Can you generalize this process for more complex expressions?
5. How does distribution work in expressions with parentheses?

Tip: Always handle absolute values before performing any arithmetic operations.