The problem asks for the scalar triple product of three vectors $\mathbf{u} \cdot (\mathbf{v} \times \mathbf{w})$. To solve this, we need to follow these steps:

1. Find the cross product of the vectors $\mathbf{v} \times \mathbf{w}$.
2. Compute the dot product of $\mathbf{u}$ with the result from the first step.

Step 1: Compute $\mathbf{v} \times \mathbf{w}$

Given: [ \mathbf{v} = [-2, -4, 4], \quad \mathbf{w} = [-3, -5, -1] ] The cross product $\mathbf{v} \times \mathbf{w}$ is computed using the determinant of the following matrix: