The integral shown in the image is:

$\int_{1}^{2} \left( 8x^{-2} - 4 \right) dx.$

Let's evaluate it step by step.

Step 1: Separate the integrals

We can split the integral into two parts: $\int_{1}^{2} \left( 8x^{-2} - 4 \right) dx = \int_{1}^{2} 8x^{-2} dx - \int_{1}^{2} 4 dx.$

Step 2: Compute each integral

1. For $\int 8x^{-2} dx$: The integral of $x^{-2}$ is: $\int x^{-2} dx = -x^{-1} = -\frac{1}{x}.$ Therefore: $\int 8x^{-2} dx = 8 \cdot \left(-\frac{1}{x}\right) = -\frac{8}{x}.$

2. For $\int 4 dx$: The integral of a constant $4$ is: $\int 4 dx = 4x.$

Step 3: Evaluate the definite integrals

1. Evaluate $-\frac{8}{x}$ from 1 to 2: $\left[-\frac{8}{x}\right]_{1}^{2} = \left(-\frac{8}{2}\right) - \left(-\frac{8}{1}\right) = -4 + 8 = 4.$

2. Evaluate $4x$ from 1 to 2: $\left[4x\right]_{1}^{2} = \left(4 \cdot 2\right) - \left(4 \cdot 1\right) = 8 - 4 = 4.$

Step 4: Combine results

Now combine the results of the two integrals: $\int_{1}^{2} \left( 8x^{-2} - 4 \right) dx = 4 - 4 = 0.$

Final Answer:

$\boxed{0}$