Determine which of the following statements is/are true:

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**.

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**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**.

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**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**.

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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**.