To find a possible rule in the form $y = k - 2 \times 3^{h - x}$ using the given point $(0, 0)$ and the additional information $y = 6$, follow these steps:

Step 1: Substitute the point $(0, 0)$ into the equation

Substitute $x = 0$ and $y = 0$ into the equation $y = k - 2 \times 3^{h - x}$:

$0 = k - 2 \times 3^{h - 0}$

Simplify:

$0 = k - 2 \times 3^h$

This can be rearranged to solve for $k$:

$k = 2 \times 3^h$

Step 2: Use the information $y = 6$ to find $k$ or $h$

Assume that when $y = 6$, $x = 0$ (if it applies to this case), then substitute $y = 6$ into the equation:

$6 = k - 2 \times 3^{h - x}$

Substitute $x = 0$:

$6 = k - 2 \times 3^h$

Now, substitute the expression for $k$ from Step 1:

$6 = (2 \times 3^h) - 2 \times 3^h$

This simplifies to:

$6 = 0$

This doesn't work, which suggests that more information might be needed, or there's a condition related to the point $y = 6$ being for another value of $x$. Could you confirm or clarify any other points or conditions for $y = 6$?

Would you like to explore this further or clarify additional points?

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Here are 5 relative questions:

1. Is there any other point given for when $y = 6$?
2. Does $y = 6$ apply for a specific value of $x$?
3. Are there any transformations in the equation that should be considered?
4. Could you specify whether the $y = 6$ corresponds to a certain point?
5. Should we explore the nature of $h$ more deeply?

Tip: When solving for constants, check if additional conditions or constraints are given to avoid contradictions.