Let's evaluate each statement one by one.
Statement #1:
\[
3 \cdot 20 = 4(6 + 9)
\]
Calculating both sides:
- Left side:
\[
3 \cdot 20 = 60
\]
- Right side:
\[
4(6 + 9) = 4 \cdot 15 = 60
\]
Both sides are equal, so Statement #1 is true.
Statement #2:
\[
4 \cdot 12 = 6 \cdot (8 \cdot 2)
\]
\[
12 + 6 \cdot \sqrt{64} = 2 \cdot 4 \cdot 8
\]
Calculating the left side:
- First part:
\[
4 \cdot 12 = 48
\]
- Second part:
\[
6 \cdot (8 \cdot 2) = 6 \cdot 16 = 96
\]
Since \(48 \neq 96\), the first part of Statement #2 is false.
Calculating the second part:
- Left side:
\[
12 + 6 \cdot \sqrt{64} = 12 + 6 \cdot 8 = 12 + 48 = 60
\]
- Right side:
\[
2 \cdot 4 \cdot 8 = 8 \cdot 8 = 64
\]
Since \(60 \neq 64\), the second part of Statement #2 is also false.
Statement #3:
\[
4 \cdot 18 - 4 \cdot 6 = 42 + 4 \cdot 8
\]
Calculating the left side:
\[
4 \cdot 18 - 4 \cdot 6 = 72 - 24 = 48
\]
Calculating the right side:
\[
42 + 4 \cdot 8 = 42 + 32 = 74
\]
Since \(48 \neq 74\), Statement #3 is false.
Final Evaluation:
- Statement #1 is true.
- Statement #2 is false.
- Statement #3 is false.
The only true statement is Statement #1.
Thus, the correct response is: 1.