The problem asks to "Draw the graph of $y = 2h(x - 4)$", based on a given graph of $y = h(x)$. Since I can't see the actual graph of $h(x)$, I can guide you through the transformation process.

To graph $y = 2h(x - 4)$, follow these steps:

1. Horizontal Shift (due to $x - 4$):

• The expression $x - 4$ indicates a horizontal shift. Specifically, the graph of $h(x)$ is shifted 4 units to the right. So, every point $(x, y)$ on the graph of $h(x)$ will move to $(x+4, y)$.

2. Vertical Stretch (due to the coefficient 2):

• The factor of 2 outside the function indicates a vertical stretch. This means that the graph will be stretched by a factor of 2. In other words, if a point on the original graph of $h(x)$ is at $(x, y)$, it will now be at $(x, 2y)$.

3. Apply both transformations:

• First shift the graph horizontally by 4 units to the right.
• Then, stretch it vertically by multiplying all the $y$-coordinates by 2.

If you have the graph of $h(x)$ available, you can apply these transformations directly.

Do you have any questions or would you like more detailed steps?

Here are five questions to expand the concept:

1. How does the transformation $y = h(x - c)$ generally affect the graph?
2. What happens if the function had been $y = h(x + 4)$ instead?
3. How would a negative coefficient, like $y = -2h(x - 4)$, affect the graph?
4. How do you interpret transformations that include both vertical and horizontal shifts?
5. Can the transformations $y = 2h(x - 4)$ be applied in a different order (e.g., vertical stretch first)?

Tip: When applying transformations, always handle horizontal shifts inside the function (involving $x$) and vertical changes (like stretching or reflecting) outside the function.