To solve the problem, let's break down the information given in the question.

We are provided with:

1. Matrix $A$ and the determinant of matrix $B$, $|B| = 4$.
2. The task is to calculate $|-2A| - |3B|$.

Step-by-Step Solution

Step 1: Understanding Determinant Properties

1. If we multiply a matrix $A$ by a scalar $k$, then the determinant of the resulting matrix $kA$ is $|kA| = k^n |A|$, where $n$ is the order (dimension) of the square matrix.
2. Since $A$ and $B$ are $3 \times 3$ matrices (from the size of $A$ shown), $n = 3$.

Step 2: Calculate $|-2A|$

1. Using the property, we have: $|-2A| = (-2)^3 \cdot |A| = -8 \cdot |A|$
2. We need $|A|$ to find the value of $|-2A|$. Unfortunately, $|A|$ is not provided in the problem statement, so let's continue assuming $|A|$ will be calculated or given separately.

Step 3: Calculate $|3B|$

1. Similarly, using the same property: $|3B| = (3)^3 \cdot |B| = 27 \cdot 4 = 108$

Step 4: Find $|-2A| - |3B|$

1. Substitute $|3B| = 108$ and solve $|-2A| - 108$.
2. If we knew $|A|$, we would substitute it here to find the answer. However, without $|A|$, we cannot compute $|-2A|$ exactly.

Answer Selection

Since we need $|A|$ to fully solve this, let me know if there is additional information on $|A|$. Otherwise, if we assume an option among the choices, we might guess based on plausible values for $|A|$ that yield results matching an answer choice.