Use the associative property to determine which expressions are equivalent

To use the associative property and determine which expressions are equivalent, we need to evaluate the expressions step by step.

First, let's simplify expression A:

**: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 \cdot -6y\)

Using the associative property, we can group the terms differently, but both sides of the equation will evaluate to the same product, as they involve the same multiplication of the same values. Thus, ** is true.

Next, simplify expression B:

**B**: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot (-2 \cdot -6y)\)

Here again, using the associative property, we are regrouping the terms. Both sides of this equation contain the same numbers multiplied in different orders, so **B** is also true.

Now let's consider expression C:

**C**: \(-3 \cdot (4x \cdot -2) \cdot -6y = -7xy\)

To check if C is true, let’s evaluate the left side:

1. \( 4x \cdot -2 = -8x \)
2. Then, \(-3 \cdot -8x \cdot -6y = -3 \cdot 48xy = -144xy\).

Comparing with the right side gives \(-144xy \neq -7xy\). Therefore, **C** is false.

Now check expression D:

**D**: \(-3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x\)

Evaluating the left side again gives us:

1. As calculated above, \( -3 \cdot (4x \cdot -2) \cdot -6y = -144xy\).

For the expression \( 18 - 8x \), we see that \(-144xy\) is not equal to \(18 - 8x\) unless \(x\) or \(y\) satisfy a specific requirement that doesn't match. However, there's no independent verification that shows equality based on the left-hand operations performed. Therefore, **D** is also false.

### Summary:
- ** is equivalent.
- **B** is equivalent.
- **C** is not equivalent.
- **D** is not equivalent.

So, the equivalent expressions are ** and **B**.