Use the Associative Property to determine which expressions are equivalent.

The Associative Property states that when multiplying, the way in which numbers are grouped does not change their product. This means that for any three numbers \(a\), \(b\), and \(c\), the following equality holds:

\[
(a \cdot b) \cdot c = a \cdot (b \cdot c)
\]

Let's examine each of the given expressions to determine if they are equivalent.

1. **Expression 1**: \(-3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x\)

To verify if these two sides are equivalent, we will calculate the left-hand side:

\[
-3 \cdot (4x \cdot -2) \cdot -6y = -3 \cdot (-8x) \cdot -6y = 24xy
\]

The right-hand side \(18 - 8x\) does not equal \(24xy\), which means these sides are **not equivalent**.

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

Using the associative property, we can rewrite the left-hand side:

\[
-3 \cdot (4x \cdot -2) \cdot -6y = ((-3 \cdot 4x) \cdot -2) \cdot -6y
\]

This matches the expression on the right-hand side. Therefore, these sides are **equivalent**.

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

As calculated before, the left-hand side is:

\[
-3 \cdot (4x \cdot -2) \cdot -6y = 24xy
\]

The right-hand side \( -7xy \) does not equal \( 24xy\), which means these sides are **not equivalent**.

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

Additionally, we can calculate the right-hand side using the associative property:

\[
(-3 \cdot 4x)(-2 \cdot -6y) = (-3 \cdot 4x)(12y)
\]

Computing this gives:

\[
-3 \cdot 4x \cdot 12y = -144xy
\]

Since the left-hand side is \(24xy\), and the right-hand side is \(-144xy\), these sides are **not equivalent**.

### Conclusion:
- The only expression that is equivalent using the Associative Property is:
- \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 \cdot -6y\) (Expression 2).