Let's evaluate each statement one by one.
Statement #1:
\[ 3 \cdot 20 = 4(6 + 9) \]
Calculating the left side: \[ 3 \cdot 20 = 60 \]
Calculating the right side: \[ 6 + 9 = 15 \] \[ 4 \cdot 15 = 60 \]
So, both sides are equal: \[ 60 = 60 \]
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 first part of the statement: Left side: \[ 4 \cdot 12 = 48 \]
Right side: \[ 8 \cdot 2 = 16 \] \[ 6 \cdot 16 = 96 \]
Now comparing: \[ 48 \neq 96 \]
So the first part is false.
Calculating the second part: Left side: \[ 12 + 6 \cdot \sqrt{64} = 12 + 6 \cdot 8 = 12 + 48 = 60 \]
Right side: \[ 2 \cdot 4 \cdot 8 = 64 \]
Comparing: \[ 60 \neq 64 \]
So the second part is also false.
Statement #2 is false.
Statement #3:
\[ 4 \cdot 18 - 4 \cdot 6 = 42 + 4 \cdot 8 \]
Calculating the left side: \[ 4 \cdot 18 = 72 \] \[ 4 \cdot 6 = 24 \] \[ 72 - 24 = 48 \]
Calculating the right side: \[ 4 \cdot 8 = 32 \] \[ 42 + 32 = 74 \]
Comparing both sides: \[ 48 \neq 74 \]
Statement #3 is false.
Conclusion:
The only true statement is Statement #1. Therefore, the correct responses would be 1 only.