Let's solve the expression shown in the image:

$15 - 4 \left| -3 - 7 \right|$

Step 1: Simplify the expression inside the absolute value

First, calculate the expression inside the absolute value:

$-3 - 7 = -10$

So, the expression becomes:

$15 - 4 \left| -10 \right|$

Step 2: Apply the absolute value

The absolute value of $-10$ is $10$:

$15 - 4 \times 10$

Step 3: Perform the multiplication

Multiply 4 by 10:

$15 - 40$

Step 4: Perform the subtraction

Finally, subtract 40 from 15:

$15 - 40 = -25$

Thus, the final answer is $-25$.

Would you like further details or have any questions?

Here are some related questions to explore:

1. What happens if the absolute value operation is removed from the original equation?
2. How would the solution change if the expression inside the absolute value was positive?
3. Can you think of a scenario where absolute values could represent a real-world situation?
4. What is the significance of absolute values in algebra?
5. How do we handle absolute values in inequalities?

Tip: When dealing with absolute values, remember they always result in a non-negative number, regardless of the sign of the input inside the absolute value.