Let's evaluate each statement one by one:
Statement #1: \[ 3 \times 20 = 4(6 + 9) \]
Calculating the left side: \[ 3 \times 20 = 60 \]
Calculating the right side: \[ 4(6 + 9) = 4 \times 15 = 60 \]
So, statement #1 is true.
Statement #2: \[ 4 \times 12 = 6 \times (8 \times 2) + 6 \times \sqrt{64} = 2 \times 4 \times 8 \]
Calculating the left side: \[ 4 \times 12 = 48 \]
Calculating the right side: First, calculate \( 6 \times (8 \times 2) \): \[ 8 \times 2 = 16 \] \[ 6 \times 16 = 96 \]
Next, calculate \( 6 \times \sqrt{64} \): \[ \sqrt{64} = 8 \] \[ 6 \times 8 = 48 \]
Now, combining both: \[ 96 + 48 = 144 \]
Finally, check the rightmost part: \[ 2 \times 4 \times 8 = 64 \]
Since \( 48 \neq 144 \), statement #2 is false.
Statement #3: \[ 4 \times 18 - 4 \times 6 = 4^2 + 4 \times 8 \]
Calculating the left side: \[ 4 \times 18 = 72 \] \[ 4 \times 6 = 24 \] Thus, \[ 72 - 24 = 48 \]
Calculating the right side: \[ 4^2 = 16 \] \[ 4 \times 8 = 32 \] Thus, \[ 16 + 32 = 48 \]
Since both sides are equal, statement #3 is true.
In summary:
- Statement #1: True
- Statement #2: False
- Statement #3: True
So the true statements are #1 and #3.
The correct answer is 1 and 3.